There were a few issues to getting it up and running.
Following the instructions I downloaded the updater and set it running, which downloaded all the needed files. However, when I tried to run it, it kept crashing out.
I had hoped this was just due to it being a 32bit binary and I was running it on 64bit. I installed additional 32bit libraries (and their dependencies) that were missing libboost-filesystem, DevIL, mesa-dri-drivers.
This got me a little further, I got a blank screen and could hear music and sound effects. When looking at a copy of the startup messages (passed to tee and dumped to a file), I saw messages relating to not being able to load various font and image files (including ones related to the menu), hence the black screen. I double checked that there were no addition files by re-running the updater, everything was downloaded.
Checking the startup messages and checking the forum, quickly lead me to this page which appeared to have exactly the same symptoms and was suggesting that this was related to S3TC (S3 Texture Compression) support.
There was a suggestion that disabling this in the config might work, however this did not work for me.
Was I missing the 32bit library that contained this support? I was, however as I was testing this on Fedora, Fedora does not ship this particular library as it is patented by S3. I could have gone and downloaded this from a 3rd party repo, but I am not happy at installing lots of extra packages from random locations.
Luckily I came across another solution when using mesa drivers > version 9 and this is to set the following variable before launching thedarkmod
force_s3tc_enable=true
This worked fine and allowed me to launch the game and start playing through the training mission.