Rime, Brothers, Beyond Good & Evil.

The Life is Strange series has already been noted, but I would also add Telltale's The Walking Dead (all four seasons constitute Clementine's story), Heavy Rain and Detroit: Become Human.
And maybe the Black Mirror series.

While the story is not bad, I wouldn't exactly call it "deep" :-)

Which is quite a feat, considering the game has no dialogues, yet still managed to tell its story.

Now I'm really curious about this game. I have to take a look. That is awesome that it can tell a story with no dialgue.