Tell ya what. I'll answer your question as soon as I find my lower jaw; I think it bounced behind the couch...
Honestly it was probably done with a seriously powerful but otherwise normal computer. If it's a tech demo, they'd probably want to do it on a computer that (technically) anyone could buy/build.
This kind of tech is going to be in the next generation of VR games. Excuse me while I go sell my son and car and house to get a Rift or Vive...
Edit:
After watching the part that's obviously someone maneuvering a "player" through the environment I can say that's definitely on a "conventional" computer. Holy hot sh*t god d*mn...