You can use https://github.com/loki-47-6F-64/sunshine which uses the same protocol as Nvidia GameStream, and you can access it with https://moonlight-stream.org/

I’m waiting for someone to make this for the Linux desktop. I would think Steam may push into it with their SteamOS project.

You can already stream games from a Linux machine with Steam and then get to the desktop. It's baked in, but I'm not sure you can directly stream the desktop without launching a game before, but it works pretty well. I managed to play a game running on my Linux desktop in the UK while being in mainland Europe ! Wasn't a bad experience at all.

You can set the Steam Link app to show the desktop when you connect.