Just a handful of fun ones off the top of my head:
- Sutte Hakkun
- PaRappa the Rapper
- The Secret of Monkey Island
1/ Enemies, spikes, stuff that crushes you
2/ You die and go to hell at one point
3/ Still has violence
4/ Anytime the planes crashes over, you can bomb stuff
The Wagyan Land platformer series (last one on SNES looks gorgeous)
Pieces / Jigsaw Puzzle
Art Style games
Anything with falling blocks (Tetris, Puyo Puyo, Dr Mario, Puzzle Bobble and their many variants/clones)
Many point and click games (adventure games besides the plot, spot the difference games, finding stuff in the pictures...)
Hudson's puzzle series for the Nintendo DS
I don't understand why you want to exclude sport games and simulation games.
A NGE-themed tamagotchi game where you raise that adamu embryo exists, and many sport games have realistic violence.
If a tiny bit of violence was tolerated, like enemies disappearing in a poof of smokes or sparkle,
I would add Kirby games, The Legendary Starfy (5), and Stafy 4.
Not the earlier games in that series since the plot doesn't shy away from violence, what's probably fish porn (really), domestic violence, death, juvenile death, reanimated dead antagonists just long enough to die again in moving scenes. There would be no way NoA in the nineties would bring these over.