I honestly don't think playing games in Japanese or watching japanese anime will really teach anybody any reasonable amount of japanese at all. Sure, you will probably pick up really common lines like ittedakimasu and ohaiyou gozaimasu or whatever. But that's really not much better than just anybody can do with a couple questions remembered to a Japanese friend.
HOWEVER, if you're trying to learn the language with textbooks/tutors/teachers/class-style, etc in addition to it. The games/anime probably wont be very significant in comparison to your own studies, HOWEVER, you will most likely NEVER EVER forget the meaning/spelling/etc of the words you learn in a text, that you also see/hear in anime/games. Furthermore, it helps with pronunciation as well. For example when I learned the word irasshaimase, I never ever forgot its meaning or pronunciation for a moment because i heard it used in the game Raccetear (and I had no clue what it meant in game before).
However, when your understanding of the language is still incomplete (I mean REALLY incomplete, as in pepole would know it's not your primary language if aliens dumped you off in their country), playing a game in that language really does reduce the fun factor for it.