FWIW, back in the day I had issues trying to stream proper PC games from my 2500k if I used h.264. Quick sync, which uses the iGPU, worked fine. Not as nice quality, but was smooth.
Most people who steam live game play regularly and make a significant living off of it actually use two separate machines. One for gaming, and one dedicated for video streaming.
The Video output from the Gaming PC goes into a capture card of the steaming unit.