You can now stream Xbox One games - including backwards compatible Xbox 360 games - onto Oculus Rift.
Microsoft just announced this new feature as an update for the Xbox One Streaming app. So long as your Xbox One and PC are connected to the same network, you'll be able to view your Xbox games in one of three virtual theaters, just like you're playing video games on the big screen (albeit in lower res quality than your TV). Think of it as VR off-screen play.
PlayStation VR offered a similar "cinema mode", which weirdly worked on Xbox One (along with Wii U and PCs, for that matter), with the caveat that you'd need to have it plugged into your PS4 running alongside the console you were using the PSVR on.