Actually averted by Katawa Shoujo: despite popular misconception that the game takes place essentially in the present, Word of God says that it actually does several years in the past (around 2007). Fittingly, for example, nobody has access to the ultra-ubiquitous smartphones of today - using old "flippables" instead.
Yo-Jin-Bo has a bunch of 1850s ronin who like to Shout-Out to modern pop culture. The technology is generally consistent with 19th century Japan, but it's never explained how they know about things like Back to the Future and Mr. T.
In Corpse Party D2: Fatal Operation, while the closed space surrounding Divine Blessing Hospital was created in 1982, various pieces of state-of-the-art technology can be found within. Since the cursed dimension has the ability to draw in and trap victims, this is Justified by Naomi speculating that whatever consciousness created the closed space is really interested in this tech and deliberately stealing it.
Aviary Attorney, set in the 19th century, likes jokes and throwaway lines that play on if they aren't outright lifted from more modern sources.
How does that American proverb go, Falcon? Don't hate the player. Hate the game.
Merde's about to go down, yo.
Ace Attorney: making the appearance of phones with physical keypads and basic LCD screens all the more jarring, rather than smartphones which are extremely commonplace in developed countries. One character in Apollo Justice: Ace Attorney does possess what's clearly a smartphone, however. In addition, many photos in early games are in black and white, but later games start involving color photos.
Burly Men At Sea is, according to Word of God, set in the early twentieth century, but has Dark Ages Norse monsters and wizards and a very twenty-first century coffee shop.