Play on your laptop using Steam's remote play, Moonlight or something similar. You run the games on that windows desktop you have stored out of the way (mine is headless as well) but play on your laptop where ever you want.
This works for some games, but for others I find the latency to be too high, and compression can get pretty wacky with games that have a lot of movement.
If you run off ethernet the latency isn't much of an issue (20ms maybe)... maybe not good for super competitive gaming, but I've never noticed any issue even with more competitive games as the network latency (game to server, not streaming) masks any input latency without problem.
