What you seem to want is simply in home streaming and steam already support this via any old pc or Nvidia shield unit for a dedicate device.
This seem to be another game streaming service.
And we simply aren't there yet.
For starters you need a roundtrip latency of less than 30ms just to barely manage a decent and responsive frame rate.
How often is your ping lower than that unless the server is very close to you physically?
And that's just two machines playing Marco polo.
let alone displaying a video feed, polling control devices, sending input to a server, that then takes input does everything to render the game, compress to video then transmit back in less than 30ms?
These things have been tried before and some even went as far as establishing data centers in most major metropolis around the world.
It gets really expensive. fast.