I think games are very much like movies in a sense. And for a movie to be good it doesn't have to be violent.
The big difference between a game and a movie is the interactive part (obviously).
Also gamer's in general tend to want challenge and sometimes competition in games, which is not the case for movies.
But "necessary" mechanics of any game, violent or peaceful are:
Achievements: People need to chase something to stay interested, a (peaceful) game that hands you everything you can get from the start would get boring very fast.
Example: If you could plant everything in FarmVille the first minute.
Reward: Once they've reached this goal they need satisfaction for the work. This could be a new feature, new items, whatever. Getting rewarded in a game activates the brains reward mechanism, which can get physically addictive, just like a drug.
Scoreboard: In today's society where everyone is judged by everyone this seems to give players alot of satisfaction, even when the only benefit is to showoff/brag. This could be counted in the reward part aswell, but I decided to put them separate.
These are three very basic mechanics that can be implemented into pretty ANY game.
Now what you have to do is to decide what kind of a game you want to create, and based on that decide how you can implement all three of these mechanics to your game.
Other points i wont go deep into:
Cooperation: It's always fun to work togheter.
Competition: Always fun to beat your opponent.
Mystery: Keeps the player curious to what comes next.
I'll end the post there since it got very long, I hope this helps you to decide what kind of a game you want to create.