In this case, the "client" would be the game render server. Your terminal -- which has the display -- is the "server."

This is already the way OnLive, for example, works. All the rendering is done on the server side, which corresponds to the Wayland/X11 client.

Cloud gaming can't work on the Internet as it currently exists. Latency is just too high and too variable, especially for consumer-grade connections when they get near saturation. When bufferbloat is a thing of the past, it might be possible.

However, even smartphones are coming with highly capable GPUs these days, so within a few years, any CPU no matter how cheap will be able to handle at least casual gaming at HD resolutions.