The worst offender is Coco Nebulon, who is literally a Surfer Chick who uses talks in stereotypical '80s slang, peppering her sentences with words such as "gnarly" and "tubular".
Chuck Rock: "Chuck is a guitarist and singer (or shouter) in a rock band along with some other cavemen [sic], his foxy blonde wife Ophelia Rock, and a long-haired dinosaur bass player; and whilst on stage he wears a long wig to hide his balding head." (TOW)
Summon Night: Swordcraft Story 2 features a robot who initially talks in Spock Speak... but the main character can't understand him and asks him to speak more understandably, so he starts talking in obnoxious Totally Radical speech. He later goes back to Spock Speak, to the relief of the other characters, and likely the relief of the player as well.
Jake from Advance Wars: Dual Strike. "Black Hole is all up in our business." Cue cringing. Or laughing, depending on the player's temperament. It gets worse from there: his victory line is "Get the plates, 'cuz you just got served!"
Waylon's very first line in Days of Ruin is a deliberate self parody/Lampshade Hanging of the NoA localization team's work with the aforementioned Jake. "Would someone tell me why these Lazurians are up in my business?". He then spends the rest of the game speaking in some kind of weird 50s hipster slang. Granted, Waylon is supposed to be an annoying jerk.
Oracle of Tao has a call shop item that summons really strange people (one of which talks about "fashions straight off the runway" when nobody even knows what that is) to buy and sell goods. One such guy sounds like a 1980s reject or Surfer Dude (to which Ambrosia tells him, "stop calling me man").
Pokémon Diamond and Pearl have people saying things such as "If you don't have Gym Badges, people think you're a total n00b, right?" and "I just got owned!" Translator Douglas Dinsdale of Something Awful put in a lot of Internet memes (like an artist on Route 208 saying he will name a painting "My Pokémon Is Fight") as injokes. Thankfully, much of the dialogue was rewritten in Platinum.
"Jock" type characters in Animal Crossing: Wild World refer to you as a "total noob" if you annoy them.
Likewise, Metal Gear Acid 2 had a nerdy Playful Hacker who used Internet slang in dialogue; unfortunately, Internet slang evolves so fast his use of it seems dated just a year later.
One word: DOOD! 3 more words: THAT'S SWEET, DOOD! "Dood" was an addition by the original translators from Atlus, but kept by Nippon Ichi when they opened their US branch. In the original, the Prinnies constantly end their sentences with ?? (ssu), a colloquial contraction of the polite copula ?? (desu).
Pocket Kingdom: Own the World, one of the very few good-by-consensus games for the N-Gage platform, is intentionally filled with this, as it attempts to mirror an actual PC MMORPG. Players buy and upgrade their weapons with "loot", and losing characters are "owned", rather than simply being defeated.
Phoenix Wright: Ace Attorney: Justice for All: "That monkey doesn't fake the funk on a nasty dunk." To say nothing of Sal Manella, the fat, geeky TV director in the first game who largely communicates in 1337-speak when agitated, prompting your sidekick to ask "What are 'suck sores'?"
Zelos from Tales of Symphonia is a milder version of this; he doesn't speak in it constantly, but when he does, it's painful.
At one point in Tales of Legendia, an Oresoren acts as the translator for a huge, toothy monster whom his people reverently refer to as a "Mighty One". He speaks its words like a Surfer Dude, hilariously deepening his voice more then a few octaves as he does so. Some members of the party naturally question whether it's actually talking that way, to which he insists that it is.
Parodied in Mario & Luigi: Partners in Time, where the plumbers encounter a Hammer Bros. duo mind-controlled by the bad guys via special helmets that talk 1337-speak. After they're freed from the helmets, they wonder who'd talk like that.
Parodied, again, in Super Paper Mario in the third chapter — which is usually referred to as the nerd chapter. The (accidental) villain of the chapter is Francis, a "high-technicaaaal" nerd who abducts Tippi thinking it's a rare insect, with no worse intent than to take photos of her to show off his new camera.
Super Mario World uses this for the Special World level names, which even for the time were likely painfully outdated to the point of sounding ridiculous. Groovy, Awesome and Funky are somewhat okay level names, but Way Cool and Outrageous sound like Narm, and Gnarly and Mondo are about as outdated sounding as possibly imaginable. As for Tubular, apart from being That One Level, the name isn't exactly slang most people on the planet would have even heard of, and trying to use that in normal conversation would merely gain a lot of odd looks from others. The level does have a lot of "tubes", though.
In City of Heroes, an officer representing Nemesis (a villain who's been around since the 1800s) tells a member of the cybernetic punk Freakshow: "I assure you, my good man, Nemesis is most definitely 'down with the street'. Word up, my homie, as it were."
Lampshade Hanging in Mega Man Star Force: When Geo travels to the AMAKEN compound, he meets a girl named "Chatty Ditz" who's, like, totally having trouble, like, sending an e-mail to her friend, y'know? When Omega-Xis asks why she talks like that, Geo remarks that "it's some sort of dialect people used 200 years ago", to which Mega responds: "I'm not sure whether this means human language has reached its high point or its low point".
You encounter another largely incoherent speaker of fluent This-Trope in the Echo Ridge vending machine, who throws around a lot of words related to coolness that were obsolete in 2000, let alone 220X.
Also, parodied in Mega Man Star Force 3. One of the noise areas is inhabited by a corrupted wave being, which has a vocabulary that mostly revolves around one word, much to the confusion (and amusement) of the player.
In Command & Conquer: Red Alert 3, the Japanese Commander Kenji will taunt you during skirmish matches with phrases like "Hey look! A noob in training." or "What? This wet nose scrub beat me?". Considering that this takes place (presumably) decades earlier in its timeline, this is probably still cutting-edge slang in-universe. How a character from an isolationist empire which has only just revealed itself to the world learned to speak in blatantly American slang is not explained, though.
In Tony Hawk's UnderGround 2, slimy movie writer/director/producer Nigel Beaverhausen talks in labored, outdated slang to the skating teams. Mainly to get the point across that he's a total square whose attempts to relate to them are just condescending.
In the English localization of Xenogears, Hammer the Supplier says, "Master, sir, did you just see my MAD SKILLZ!?"
Need for Speed: Underground 2's use of street slang was criticized when it came out; more than a decade later, and some of the dialogue is just downright painful to read or listen to. The most prominent example is that the in-game currency is called "Bank".
Griffith "Griff" Simmons' speech in SSX 3 was... painful. And, indeed, he does say "TOTALLY RAD!" as he's hitting a particularly awesome trick. Not to mention Mac Frasier's terrible street lingo, which aged pretty pathetically. Yeah, Mac, we can say "bling bling." But nobody has wanted to since 2004.
Bad Dudes: "Are you a bad enough dude to rescue the president?"
One of the villains in Sly 2: Band of Thieves is Dmitri, a French Jive Turkey lounge lizard who learned all of his English from American music videos, and communicates in a mish-mash of outdated slang. Eventually lampshaded after Dmitri delivers a convoluted threat right before the boss fight with him, and Sly retorts with "I have no idea what you're saying. And your suit sucks!"
The Sims 2 expansion pack Teen Style Stuff evoked this trope in their Recurring Gag: Like, totally reticulating splines, dude.
Suikoden V features Lu, a hyper teenage girl who uses 1337-speak and emoticons in her dialogue.
Take a shot every time you see or hear the word "extreme" in NBA Jam Extreme. By the time you're halfway into playing the Vancouver Grizzlies, the first team you face in Arcade mode, you will be too drunk to continue. At the very least, they spell it properly.
Data East USA localized Kaiketsu Yanchamaru for the arcade/NES as Kid Niki Radical Ninja, though the "rad" makeover affected little more than the game's title and the protagonist's hairdo.
In one death of Space Ace, Dexter says, "TOTALLY COSMIC!" Only then does the Star Pac go boom! As ace, he sometimes says "Oh, far out!", usually in other death sequences, but he also says it in at least on regular gameplay sequence.
Radical Rex: On the Super Nintendo: "Rad-rad-rad Radical Rex! / Radical! Excellent! Awesome! Legendary! / He's so rad he's so rad he's my real cool Radical Rex! (Radical Rex!) / He's so rad he's so rad he's my real cool Radical Rex! (Radical Rex!) / He's so rad he's so rad he's my real cool Radical Rex! / He's my real cool Radical Rex! / He's my real cool Radical Rex! (Radical Rex!)" The Sega CD intro is debatably better.
Borderlands 2 DLC Mr. Torgue's Campaign of Carnage has Flyboy, a 16-year old pilot who's constantly taunting his foes with some kind of weird slang that mixes Leet Lingo with Final Fantasy references with such terms as "Tough Tidus" or calling his opponents "Hojos".
Iggy's Reckin' Balls is written almost entirely in outdated slang. However, the tongue-in-cheek and not at all serious nature of the game suggests that this trope was intentional on the part of the writers.
Jimmy Lightning from Peggle considers himself a "rad scientist", and talks entirely in this style. When the player makes a particularly good shot, he will make comments such as "Mad skillz!" and "Tubular!"
Life Is Strange is an interesting example in that the slang is not particularly out of date, just overused or used in odd places ("You got hella cash", "You hella saved my life", "Are you cereal?", etc). A few reviewers and fans have noted that the slang itself appears to be used correctly - instead, the audience hearing it is out of touch, and thus assumes that it is being used incorrectly. However, by the time Episode 4 arrived, the writers had listened to audience criticisms and dialed back on the slang. But "hella" stuck around as sort of a Verbal Tic for Chloe.
Splatoon is very, very unabashedly retro-'90s in everything it does. Even the tutorial sequence is thickly saturated in ghetto-fabulous slang. Funky fresh! Characters even unironically use 'radical' in a 2015 game, for example when Callie says "I just saw the raddest car drive by!" in the European translation (in North America she says "I just saw a SUPER fresh car drive by!").
In particular, fresh gets used the most, including in the Squid Sisters' sign-off catch phrase.
The victory screen for winning an amiibo challenge has NOICE plastered in graffiti style letters on it. This is probably the least dated slang in the game. The boy amiibo also calls you "playa".
This is Played for Laughs in-universe. Callie overuses early 2010s slang in the announcement to the North American Snowman vs Sand Castle Splatfest. Marie lampshades how ridiculous she sounds.
Callie: Team Snowbae is so fleek I literally can't even! It's cray. Like... crayfish cray.
Marie: ...I was gonna go snowman too, but after that...
Chip's Challenge has some painful attempts at nerd slang peppered into the between-level messages, including the use of "computer breath" as an insult.
The Learning Voyage series has ZZ, a girl who's supposed to be the "cool one". She greets players who enter the "Hall of the Wild" exhibit hall by saying, "Dudes, dudettes...", and she introduces herself by saying, "Yo! ZZ in the Craft!"
Final Fantasy VII's English localisation has a lot of slang in both party dialogue and NPC dialogue. It was a big achievement at the time of release, signalling that the game was Darker and Edgier than its more stilted competitors - and there was swearing in the script, too! Unfortunately, a lot of the script now comes off as painfully 90s (Yuffie's Valley Girl speech) and lots more just painful (virtually all of Barret's dialogue, as well as Cait Sith's and at least a chunk of Cloud's). Cid's dialogue is intentional Curse of the Ancients, though, and still funny. It doesn't help that, while all the player characters have very clear and diverse manners of speaking, the 'slang filter' means that a lot (although by no means all) of the NPCs talk in the exact same way, whether they're from the slums of the world's biggest metropolis or minor nobility in Wutai.
The decision to localise a monster referred in Japan as "Funny Face" to "Dorky Face" is the sort of thing that would only have happened in 1997.