I felt sad when I finally completed Braid. It's still one of the best games I've ever played and I knew I was never going to find something like that again. This paper brought me back to that sense of wonder that I had the first time I played Braid.
That very last stage stands in my memory as one of the best uses of game mechanics as part of the story telling I've ever seen. It's the rare sort of thing that truly makes games an art of its own, rather than some sort of "interactive movie".
Ludonarrative resonance. It's fun to see the critical/theory sphere develop alongside the medium. We sometimes forget just how young videos games are. Compared to film, they're completely in their infancy, and narrative film isn't even 100 years old yet.
I can't think of many other games where the mechanics themselves reinforce the story. Papers, Please does it pretty well.