A lawn mower game. It's like those games where you use the money you earn to keep buying better gear to cut lawns. The lawns and landscapes get more challenging, from steep inclines, to squirrels that get in the way, and people leaving garbage and old cars in the lawn (but not to the point of absurdity). You earn more when you decorate the lawn more, and start landscaping.
A snowball fight game. A multiplayer game that plays like japanese dodgeball games, like dodge danpei. However, you wouldn't use the super throws willy-nilly, because if other players catch your super throw, N number of times, they'll end up learning it, and can use it on you. You can also build snow walls, forts, etc. during the course of the match.
A time-traveling superhero. A simulated city, where a bunch of crime will take place, and it's up to you to try to save as many people as you can. You can rewind time and redo things, but the things that you do will have other side effects and outcomes that affect your ability to save someone else. In the end, it's clear that no matter how powerful you get, you won't be able to save everyone and some citizen is going to be mad at you. Pick from other time power heroes, that can replay time with another body, or another one that can slow down time.