Game playability depends on network bandwidth and latency and also on the type of game. I’ve played Hitman Blood Money over the net when Square Enix had a programme that let you play their games in a browser for 30 minutes or something for every ad you watched and that worked quite well on a 12mbit connection close to the servers. So low bandwidth, low latency. But I can’t imagine something like Counter Strike working well.

But no matter what happens the desktop can’t die as there are still Linux, BSDs and MacOS (maybe even Haiku but I don’t know how viable that is, certainly not for gaming anytime soon).