To run Xorg application in docker you just need to mount the Xorg socket into the container. First you need to disable access control so that the app from inside the container can connect to the Xorg socket with
After that you can run the container and mount the socket:
docker run -it --rm -v /tmp/.X11-unix:/tmp/.X11-unix -v $PWD:/home -e DISPLAY=unix$DISPLAY \ --device /dev/snd --name pygame3 olafgladis/python3-pygame python3 /home/app.py
The important part is
-v /tmp/.X11-unix:/tmp/.X11-unix. If you want to write your pygame application in python3 you don't have to compile pygame yourself, and just use this docker container. The Dockerfile for it can be found here. For the a small demo I provided also a small snake app and a bash script to start in inside the container.
Afaik this will only work on linux.