I don't play too many games, but 2 "anime style" games that I like are
Knock Knock and
Prune.
They are stylistically both very attractive and the play is very nice. However, they are also from opposite ends of the spectrum.
Knock Knock is an immersive creep fest. It's filled with nightmarish imagery, haunting animation and music and is full of surprises. The dev recommends playing it lights out with headphones on and I agree. Super intense. Gives you some nice shivers.
Prune is meditative and starkly beautiful. It's half zen, half game. The simplicity of the goal is deceptive and play takes you through some interesting puzzles. I find it a great way to put myself in a state of zanshin as I get drawn in. You'll find yourself totally absorbed and impressed by the aesthetic.
Both are pay to own, but are worth every penny, IMHO.
Good even on repeat and you will want to go there again. Not a lot of "action," but they are addictive and mood setting.
BONUS: Both are UWP and you can play and pickup your progress across WP 8.1 / W10M / Windows 8 or 8.1 / Windows 10 and Windows RT.