I conveniently had my UT04 retail box sitting on the shelf next to me. I can confirm there's a little penguin on the back of package, and under OS requirements they list Linux with an asterisk explaining it's not supported by Atari (publisher).
There is nothing else in the manual indicating how to use the Linux version, which disk to use, or any additional information that I can find.
Edit: geez I miss game manuals sometimes. All the game mechanics are so nicely explained, and it has instructions to setup modding tools!
Epic shut down the UT2004 master server back in this spring, before it died the community had created a new public master server, I had to edit the master server address in ut2004.ini but it works.
Epic does deserve credit for running the master server for a game for 19 years, regardless of their current actions, that deserves mad respect.
They even ran their stats tracking service untill then IIRC...
About ten years ago, I switched to Linux, but two years later I switched back to Windows for gaming, I didn't want to have to deal with gaming on Linux and fiddle with settings to get it all working.
I know that things have changed and that gaming on Linux is far better now, but as I now work mostly in Windows, I am just too comfortable with it to switch again right now.