What do you mean by this? A game taking place in Japan, or having japanese culture ties that wouldn't make sense made anywhere else?
I got one that fits both those:
1st place: Tokyo Jungle
Takes place in tokyo japan, and you play as different animals you unlock. You mate and take over territory. Its an amazing game, unfortunately, it's download only and locked away on PS3.
Sony never ported it to ps4 so we never got to play it and never got a sequel, that it so deserved.
There were a few other games on ps3 that were Japanese centric
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Runner up:
Noby Noby Boy: I mean come on ,... just look at the screenshot.
You could say Yakuza and all that, but that's an easy way out, they are more take offs from GTA and shenmue respectively.
3rd place goes to: Devil Summoner 2: Raidou Kuzunoha vs. King Abaddon - the ps2 game I bought near the end of the lifetime. It came with a stuffed animal vampire thing. Was original awesome game. I never did get the first game though (should of both are worth tons of money. )