As someone who isn't familiar with game development, could someone explain what exactly is and isn't free? What happens if I try to run the game without the Doom3 media? How might one go about making their own media for the game? Does it even make sense to do so? How tightly coupled is the released source code to the media?
The source to the game executable (rendering, script interpreter, physics, pathfinding) is free and released under GPL. The assets, however, such as scripts, textures, shaders are still under the original commercial license.
It is certainly possible to make your own media for the game; it will be a lot of work, but arguably less work than writing your own game engine AND making the assets. It makes sense because the Doom3 engine is very flexible and you can do a lot with it, some of which has already been done in the form of mods (as the SDK has been available for a long time).