For the category, I agree. We already have 3 major games and I doubt that it will stop there. Though choose the category name wisely, as we do have in-series games as well. I recommend adding "adaptation" or something to the category name to avoid ambiguity.
For the infobox, I'm wondering if we should change "kanji" to just "Japanese", since all the game names are usually entirely in katakana and we then get people who try to change things and mess up the functioning of the infobox.