AFAIK, it's possible to forward X-Window sessions, i.e. a computer ("client") may work as a (dumb?) terminal for another ("server"), displaying the desktop, GUI, etc. (and playing sounds, etc.) This means that the programs are actually running in the "server", but they can be used in the "client", hopefully with a negligible delay due to the LAN.
I am uncertain about the resources that this requires in the server and the client and what is the information that is actually transferred over the network, that is the question and that is what I would like to know.
More clearly: What are the responsibilities of the server and the client? What is the resource consumption in both cases? What kind of information is transferred over the LAN? How much bandwidth does that require?
Why are these questions important? The purpose (maybe) is using a Raspberry Pi or a similarly inexpensive computer as a terminal for a good computer, allowing several persons to use the big computer with their own monitors, keyboards and mouses simultaneously (most of the time I'm using less than 15% of my processor, less than 25% of the RAM, etc.)
An example use case to consider is the feasibility of watching a YouTube video. Points to consider are whether video and audio will be correctly in sync, the framerate will be smooth, etc. I'm not sure whether the rendering happens in the server or the client (and how) and therefore the consequences. Render in the client may require too many computational resources, render in the server may require too much bandwidth.
Another example can be playing a flash game. This is not needed, but it may be illustrative of the limitations.
I think Valve is trying to achieve something similar, I don't know if there is much progress in that regard or something to look forward.