Flower and Journey by thatgamecompany are short but masterclasses in telling story. Limbo and Inside might also fit your definition. They're dark but non viole

Flower and Journey by thatgamecompany are short but masterclasses in telling story. Limbo and Inside might also fit your definition. They're dark but non violent. Sackboy, Tearaway and Little big planet do have you defeat some baddies but they're also avoidable for the most part.