I don't know what you mean when you keep using the words
"proprietary driver." Do you mean Vendor supplied? DDO has no video
drivers of its own. Period.
Proprietary is the correct terminology for Linux drivers.
LINUX is its own special case -- not only is there no such thing as
"LINUX," but software which woks on one Vendor's version of LInux
will not necessarily run or behave the same way under another
version. Why am I calling it a "special case?" Because each
version's supporters not only believe that their version is the best
(a totally reasonable belief) but that any "linux software" should
work on their version. (And I must admit, I have never heard of the
"Ultramint" version so I know virtually nothing about its
"functionality," or how it is similar to, or different from, other
versions of Linux.)
I would recommend taking your Driver question(s) to the support
forums for Ultramint. You're likely going to need seriously detailed
(in depth) technical advice on this one. And/or visit the WINE
support forums (winehq.org) and their video section. You might get
support/an answer from the LOTRO forum at WINE:
http://appdb.winehq.org/objectManager.php?sClass=version&iId=23486
This is very inaccurate. There is indeed only one Linux - a single kernel. As for GNU/Linux, there are several distributions, but they are for the most part binary compatible, within reason, though special care obviously has to be taken to get proper relocatable binaries. Proprietary drivers are designed to be portable between distros, as is Crossover (though they limit which they "officially" support, though that usually does not matter much in practice).
Like I said the confusing part is that DDO will run in windows, but
not in linux on this machine.
ATI's drivers for Linux have generally been somewhat lacking. I doubt there is any chance at all of getting any heavy 3d game to run with the free/open drivers. The free ones are usually ok for desktop use, but not very useful for gaming. You need to get the proprietary drivers installed. Here you will need to consult the distro's documentation, as they generally have packages for these. If it's mint based, that is in turn Ubuntu based (which in turn is Debian based, ahem), so you should be able to follow instructions for those distributions. I'm on Debian here, and not on ATI, so I can't help much, though I keep seeing "Hardware Drivers tool" mentioned in documentation, so perhaps that could be a place to start. Otherwise, like William said, the distros forums, wiki or IRC channel are your best bets.
Also, as for the whole "runs on Windows, but not Linux on the same machine". Keep in mind that Wine/Crossover needs to translate all calls to the Windows API to their Linux/POSIX equivalents, and the layer is in no way complete. It also needs to translate Direct3D to OpenGL, which in turn relies upon the graphics driver - in short there are several things that can be different making stuff that runs on Windows not run on the same machine in Wine/CX :).