I have seen some videos about non combat games, some platformer examples where bit-trip runner, vvvvvv, super meat boy (is violent but you don't fight anyone), flow, portal (first person puzzle plataformer shooter... there was someone who made a portal base labyrinth platformer game here just don't remember what it was called), one called and jet it moves, to name a few.
Basically is about plataformer mechanics and the goal, for example the character could be some kind of nature daemon (god send), that needs to reach areas in order to restore the land after some weird event turned into a wasteland, restoring certain areas will change them allowing for improvements on its jumping skills to reach further.