I heard that the reason why music identifiers don’t work offline is because their databases are huge, with millions of songs (including video game music). Databases containing only video game music may be significantly smaller, even if they contain the soundtracks of over 1000 games.
In terms of raw horsepower as well as storage, probably. People were already doing audio fingerprinting in the early '90s on, like, 386 hardware. It ought to be trivial for anything even vaguely modern. The entire fingerprint data for a 2 minute chunk of audio is 3-4 kB or something. I don’t even think the size of the database will be hugely onerous.