Honestly, prepare yourself for a real struggle when playing games in Japanese. The average Japanese second grader is going to have a vocabulary much much larger than you're likely to have without at least three years of language study, so expect to be using the dictionary a lot. Moreover, the grammar will often be above your understanding. I find that by the end of Genki 2, or JLPT N4, you have enough working grammar to understand 95% of what's said in non-RPGs/VNs (but nowhere near enough vocabulary). Until you've gotten your studies to that level it's going to be immensely frustrating, as you'll be dealing with both grammar and vocabulary you don't understand.
Until your grammar skills are stronger, you may want to just play some really simple games where you don't need to read in order to progress, and just get some repetition from reading level select and menu screens.
That said, some games are really excellent for acquiring and reinforcing vocabulary if you're willing and able to stick with it.
Harvest Moon may be good, but I don't know if they actually have Furigana. The newest one doesn't, I'm pretty sure.
Animal Crossing has furigana and you can pick up a ton of vocabulary from all the items and neighbors. Be warned that very few of them speak "textbook Japanese" so you'll be dealing with a lot of casual speech and different "accents." You can get by pretty well without understanding everything though, so it's a pretty good immersion game.
Yokai Watch is pretty good too. Lots of dialogue, aimed at kids so it's very simple, and the game is dead easy so you don't need to put too much time into understanding the tutorial popups if you don't want to.
TLDR: Play games with no "required" reading for now, get Animal Crossing if you want a challenge.
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