Can I use my laptop to play games on my PC?

Sorry if that makes no sense, so I will clarify here. What I was wondering was whether I can run a game on my PC (upstairs) but control it on my laptop downstairs through our LAN.

The reason I want to attempt this is that I read somewhere ages ago that they were going to create a console system that run similar to this: where all the graphics calculations were run on an external device and sent wirelessly and I was wondering whether the software allowed for something similar now.

Is it as simple as just using a remote desktop application, or do I need something else?

Thanks,