Basically, the game runs on a server, not anything you own. You're connecting to some server owned by Google that runs the game, and streams the image to you, so nothing on your end is doing any work other than sending inputs to the server, and receiving and displaying the rendered image.
I don't think it's a terrible idea in theory since it removes the need for you to own a powerful gaming PC or whatever, but then it gets into all sorts of other questions like the sort of internet connection you'd need for something like that to work (apparently the service requires 25 Mb/s download speed to render at 1080p, and there's also the issue of input lag which makes stuff like fighting games basically unworkable through a service like this), ownership of the games, what happens if Google decides to simply drop a game from the service, and so on.