It's been about 15 years since I played it, but I recall the writing in Braid being memorably shallow, clumsy, and pretentious (with the grand twist at the end being that they guy who spent the whole game acting like a clingy stalker was actually a clingy stalker this whole time).
That wasn't the real twist, the real twist is that it was all an allegory for the Manhattan Project
I very deliberately did not say anything about my opinion about the quality of writing in Braid (and I think replaying it again wouldn’t do it any favors) ;)
But I do think that the writing was fairly central to the intended experience and design of the game.
The actual story wasn’t anything special, but I thought how it told the story through mechanics was really well done. It wasn’t the first to do that but did it a larger scope than anything else at the time.