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. 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).
I agree, though I also believe that Reddit is like that already.