I tend to not like story, so the following might fall short of the story aspect:

* Fez

* Overcooked

* Animal Crossing

* Untitled Goose Game

* Baba is You (maybe?)

* Snakebird

* Stephen's Sausage Roll

* The Witness

* Rock Band (or it's ilk)

* Bernband (haven't played but looks interesting)

* Slime Rancher

* Mini Metro

* Journey

I would recommend "Unrailed" but there is a bit of violence with the robbers that come in that you can kill.