There are always these...

...which I happen to love.

Just because they aren't depicted in the most gruesome way doesn't make them any less violent, they're still hurting others. What OP is asking is complete non-combat like the ones he mentioned.

I would say ios is your answer. The top 100 mobile games are littered with non-violent games.

Mario is definitely a violent series and I'm baffled that no one mentioned that he shoots fireballs at living creatures. Hell Yoshi eats enemies alive (and turns them into eggs).
Just because there isn't blood doesn't mean it's not violent.

Most of P&C Adventures genre is non-violent...but yeah, people just like shooting/hacking stuff in video games.

In board gaming, for example, it's quite different...when someone says that certain game is Eurogame (does not necessarily comes from Europe), and there are LOT of Eurogames out there, it's pretty certain there is no direct conflict in it, or it's kept to minimum.

Meatboy and FEZ and non-violent experiences. In fact, you can find lots of successful platformers and puzzlers that don't require the player to engage in acts of violence.

There is, but just not as big

Puzzle games, VNs, simulators, rhythm games, etc.

I think the first question that needs to be asked is clarification of what you mean by 'violence'.

Does it only refer to combat, such as in first person shooters? Or does can it refer to acts of violence that aren't necessarily enacted by the player? For example, I just played the latest Ace Attorney game, and while I never once shot a person or selected an attack option, violence still had a role in the game's conflict as I investigated murder scenes.

The Sims is the PC's best seller. Games don't need combat to be successful, but, the average they will be more successful with more interaction. Action is an easy way to introduce interaction to a game.

Hippy friendly games do better on mobile.