What if the gaming PCs were in orbit? You could have the orbit of the satellites track the sleeping times of populations, so that you don't have PCs above areas where nobody would use them.
Starlink promises latency around 20-40ms, so I do wonder if this is possible. You would have far more distance between the client/server, but I would expect that routing would be greatly simplified.
Starlink gets that latency by orbiting close to the Earth. At 525km, a Starlink bird completes one orbit in 95 minutes. For a twelve hour demand response orbit they'd have to be around 20000km high, more than one Earth diameter away, giving a far worse speed of light delay than just talking to a server one continent away.
Powering and cooling tens, hundreds of gaming PCs in orbit is beyond infeasible right now. RTGs can't produce that much power even if we had the plutonium. Solar panels are too big and heavy and don't work on the dark side of the planet. Batteries to complement the solar would also be prohibitively heavy.
Starlink promises latency around 20-40ms, so I do wonder if this is possible. You would have far more distance between the client/server, but I would expect that routing would be greatly simplified.