In Display Settings, HW Acceleration is grayed out because that program doesn't understand how the nVidia drivers work. So it won't let you enable acceleration with it.
This is actually a good thing, because if it did let you select it, it would actually disable hundreds of working desktops when people clicked it.
Anyway, since TuxRacer runs, you do indeed have OpenGL, but Wine needs a bit more than that. Wine requires some headers that binary installations of TuxRacer don't, that you may or may not have. Check the output of wine's configure script for some hints on which files you need to get to fix that one. Probably GL/gl<something>.h. Also, the config.log file that the configure script creates might have some clue as to what's going on -- whenever a test fails, the config.log gets a copy of the failed program, plus the command output.
There is only one UT2003 version, and it contains both Linux and Windows clients (though that isn't advertised; it's a shame, but the box art was already being printed when the Linux client made it onto the CDs). I've got it too; the way I would set it up is do an export SETUP_CDROM=/mnt/cdrom
(but change this if your CD drive is mounted somewhere other than /mnt/cdrom), then from the same shell session, with CD 3 in the drive, do a mount /mnt/cdrom && /mnt/cdrom/linux_install.sh
. This will first mount the disk, then run the installer.
The export SETUP_CDROM bit is so that the UT setup stops chugging at your floppy drive thinking that that's where it should get the setup info from. For some reason, it's not great at detecting which mount point is your CD drive. Other than that, though, it works pretty well.
Once you've installed it, then you're going to want to run loki_update
as whoever you originally installed UT2k3 as, so you get the most recent patches for it. You have to run that as the same user because the original setup symlinks an XML file into the home directory of whoever runs the setup program, that describes what's installed.