Because they don't have to run a large operating system at all times. Perhaps I'm overestimating how much this works them, but I was under the impression it wasn't insignificant.
You are vastly overestimating the amount of CPU required to run Windows. When you are gaming, its probably 1% of usage.
As I sit here, my CPU is at 2-4% and my memory is at 20%, the vast majority of which is tied up in the large amount of Chrome tabs I have open.
Can you buy games if you don't have a PC?
Yes, just log onto the Steam website on Thursday and buy games. You can even use the mobile app to purchase games as well.
You can then play them later when you have access to a PC.