Use OpenJK

[isair]

https://github.com/JACoders/OpenJK

Fetch and build from source while building the docker image.

[Razish]

I was about to mention something along the lines of having a traceable path from source code to executable binary, fetch+build is a good solution for that :)
You could also piggyback off the official builds for each platform. The buildbot is publicly accessible and contains the full stdio of fetching, building and uploading the build results. This would reduce dependencies on the Docker image.