Fantasy Biologist. Green squares are plants or slimes - photosynthetic organisms, red squares can be salamanders, dark grey bats, and so on. Make their AI search for food and sleep, sex and shelter, all with the idiosyncrasies in their genome. Make them kill each other and make it fantastical, salamanders spitting fire and slimes splitting up. You can render combat with colored squares too.
The player is a biologist, walking around studying these creatures, basically an observer. You can add interaction things for the player, like giving food, healing or murdering, but in principle the creatures will ignore him. There can be a bestiary to complete and some quests, but it'd be basically an spectator's game.
Turns advance by player's actions.