The Dutch Flash game Bouterdart ("Gnome Darts") features a catchy theme song in which the gnomes sing about how they're not as famous as other fictional "little people" like The Smurfs, and have to make ends meet by letting people use them to play darts.
God Hand qualifies, although the song itself actually plays during the ending credits. ("Lost a limb/in a fight/but don't worry babe, I'll be cool/the ultimate/power of a god/is now my secret tool")
Take a listen to "Still Alive", played at the end of the game Portal. This catchy, sweet-sounding, yet also slightly sinister song pretty-much sums up the plot of the game.
Similarly, the theme to the spoof Flash platformer You Have to Burn the Rope tells you exactly what you just did.
Then Portal 2 does the same thing with the song "Want You Gone". "So here we are again, it's always such a pleasure. Remember when you tried to kill me twice?"
As the credits role on Call of Duty 4, lead animator Mark Grigsby raps about the events of the game in character as Staff Sgt Griggs. He actually had a burgeoning rap career before joining Infinity Ward, so it doubles as The Cast Showoff.
Final Fantasy X for the song Otherworld. "An Other-world awaits you", "and you will fight, fight, fight... fight, fight, FIGHT", "Go now, into the sand and dust in the sky, go, for it is better to do than to die".
Final Fantasy XIV gets in on the fun with the boss theme for Shadowbringers, Insatiable, which describes the plot of the expansion.
''The road that we walk Is lost in the flood Here proud angels bathe in their wages of blood At this, the world's end, do we cast off tomorrow!
Persona 4 and its theme song for battles, Reach Out to the Truth, qualify for this trope. The entire game, for instance, is about seeing through the lies that cloud the truth from one's eyes, both self-imposed and those that cloud our view of others. Within the chorus, the lyrics include gems like "Oh god let me out / can you let me out / can you set me free from this dark inner world / Save me now, last beat in the soul". The majority of the game is about venturing into dungeons full of shadows - dark, repressed inner emotions given form - to save whichever character has been kidnapped that month.
''Dragonborn! Dragonborn! By his honor is sworn To keep evil forever at bay! And the fiercest foes rout When they hear triumph's shout! Dragonborn, for your blessing we pray!
Grand Theft Auto: San Andreas brings us a rap song summing up the basic story behind CJ, and some explanation about the game's defining elements.
The theme for Metal Gear Solid 3: Snake Eater sums up what you have to do over the course of the game while still sounding like something out of a James Bond movie.
Octodad: Dadliest Catch features "Octodad (Nobody Suspects A Thing)", setting up almost the entire plot (except for the deranged sushi chef Big Bad).
Who's that man in the three-piece suit? Making a doll with logs and fruit? Who's that man with the eight strong legs? Tried to make breakfast, but he broke my eggs
Octodad, nobody suspects a thing Octodad, he's got a good thing going on Octodad, nobody suspects a thing Octodad, Octodad
Rock Paper Scissors Champion, as featured in a Jim Sterling Best of Steam Greenlight video here, has one that has to be heard to be believed. And yes, the game is what you think it is.
Armikrog sums up why exactly the protagonist is on a Death World planet in the game's opening cutscene:
The people of planet Ixen Are surely going to die Without the power of P-tonium found On planet Spiro 5 Our hope was brother astronauts Vognaut, Numnaut and Tommynaut. Two are dead, Tom's all we've got This kid is green, do we have a shot?
Cyber Grannies opens with a song by Atoz and a sentient airplane explaining that the grannies are called Cyber Grannies because they live in a computer. The song also promises words to learn and games to play.
Kinda bug and kinda snak Try to catch them in your trap Feed somebody and you'll see we are whatever we eat! Find them hiding in the sand Tearin' up a ketchup patch Come to Snaktooth Island and discover: It's Bugsnax!