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How is the GUI accessed? X11 socket sharing? Because I guess that for gaming both X11 over SSH and VNC would not perform very well...

The same way as every local application is accessing it, via a Unix domain socket /tmp/.X11-unix:/tmp/.X11-unix / DISPLAY=unix$DISPLAY :-)

This will give you a frame rate identical to your host, so there is no overhead running your 3D apps in the container.

Is there any overhead at all in using Steam (or anything) through Docker?

I'm not very familiar with using Docker.

The overhead is negligible (close to 0). ;-)