This game helps you learn Kanji, but also some of the other "alphabets" of Japan. With practice you'll be able to read!

This seems to draw from several cultures, and has a very definite "Asian" influenced area in what I've gotten to play so far. The quests are intruiging.

This is not "Asian" but does involve a lot of strategy. To me it's a bit like a game of Go but with more players. Not completely, but enough.

While not Japanese, there are thought to be ties between Ainu peoples & culture, & the native Inuit peoples & culture. The spirit world theme also fits.