The game is rendered remotely and broadcast to one or multiple clients that display the output and handle the input. The network introduces a massive round-trip (input -> network -> remote -> network -> display) latency compared to running the game locally, so it's only really viable for most games where the internet infrastructure allows it (so Australia and much of Europe are out). The advantage is that the remote VM can be significantly more powerful than a local machine.
The early service was both an experiment/development version and a loss leader to get people to join the service in the first place. Price hikes and free service degradation were planned and inevitable.