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I probably would file it under Different World, Different Movies.
Could be both, Future Slang is actually broader than it sounds (Star Wars and some fantasy examples are included), Language Drift could be included if the game shows or implies the background for how those terms evolved.
Different World, Different Movies seems to be exclusively for media; though Hypnospace has examples of that trope too, i don't think this particular case counts. from the looks of the examples on Future Slang, i think it probably fits best there (another Alternate History example, Command & Conquer: Red Alert 2, is listed). it doesn't explain how the slang diverged but since Hypnospace is Like Reality, Unless Noted it isn't super difficult to imagine
would a case where slang diverges in an Alternate History be Language Drift or a downplayed version of Future Slang? i'm looking to add an example about the slang in Hypnospace Outlaw, which is set in an alternate 1999 with different internet lingo (for example LOL is replaced with BWL, "bursting with laughter")