The common thread here seems to be issues with what you mean by an 'anime' game.
However, I think that the idea of classifying a game due to art style is idiotic. You may as well classify it by what style of music the game uses for it's soundtrack.
Play games you find fun. If other people think it's childish, forget them. You don't need to justify yourself for enjoying video games anymore than other people have to for liking sports, cars, or guns. In the end, video games are a hobby, like any other.
That said, I do play games with an anime aesthetic. Hell, you can probably tell that by my user icon. I've beaten every translated SMT game, every windows Touhou game, played Ar Tonelico 1 and 2, Atelier Iris, and Mana Khemia 1 and 2. I've also beaten Serious Sam at least a dozen times, beaten Doom 1 and 2 on Ultra Violence, loved the hell out of Modern Warfare 1, and am currently playing God of War 3 on Titan. Not bragging(okay, a little on some of it), but frankly, in the end, they are *games*. It is a hobby. If you are ashamed of or childish for buying games because of an 'anime' aesthetic, don't buy them or get over it.