i7 5820K @ 4.25GHz | EVGA GTX 1080 SC | Gigabyte GA-X99-UD4 | Corsair DDR4 3000 32GB | Corsair HX 750W
SSDs: Intel 660p M.2 2TB, 3x Samsung Evo 1TB | Startech PCIe 4x USB 3.0 | Startech PCIe 2x USB C 3.1 gen2
Why do you want to stream it?
I would think that the local PC that the Rift is connected to would have to handle the head tracking to avoid latency issues. Network latency wouldn't be a problem for the game inputs (controlling the game on the big virtual screen), but the VR Cinema app would need to run on the directly connected PC, and thus, that PC still needs to be powerful enough to run a decent VR experience. If the local PC can handle that, I would think it can also manage to run on old game on the VR Cinema screen directly.
Steam streaming shows the desktop of the remote PC (stream source) on the local PC (stream receiver). To stream a VR experience that way, the remote PC would have to handle everything, and thus you would have network latency between moving your head and seeing the motion reflected in the Rift. I don't think Steam streaming is going to be useable with the Rift.
My VR system is set up to do something similar. It requires two machines though. One machine plays the game with the video output into another machine's video capture card, which puts that video on a virtual big screen. It's very low latency with 60fps in both the game and the VR environment.
Look at my thread. It contains a demo video of me playing Dota 2 on a virtual big screen.
Even with a beefy computer and a simple 3D game, it might not be possible to play the game and the environment on the same computer at 60+ fps. Using two machines makes it easier to reach 60+ fps.