Well, I haven't paid much attention to these gaming products, but this is a really clear example of the difference between remote display and remote rendering.

This Google Stadia is using a remote display protocol. All the rendering is happening in the machine in the datacenter, where the CPU and GPU lives and the game executes. It's a bit like someone sitting in the datacenter playing the game while you live-stream it at home, except they also pass through input controls so you can steer the game from home instead of just watching it.

A remote rendering protocol, which is no longer really sensible, would try to keep the GPU in your living room while running the game in the datacenter. Instead of streaming the screen updates at a nice steady pace based on your display resolution, it would have to stream the drawing commands from the datacenter to your GPU, adjusting the geometry as the game simulation updates the world model and stalling with nice loading screens every time it needs to shuffle in different texture and model data from the game computer to your GPU via the internet.

Thank you. I really get it now. You have a fantastic gift for educating!