http://bugs.winehq.org/show_bug.cgi?id=12186
--- Comment #3 from Emmental onshin@yahoo.com 2008-03-25 07:17:33 --- The game client can be downloaded from the FTP site: ftp://ftp.playtr.com/
This should allow you to see the loading screen bug, but will not allow you access to the game beyond the login screen for bug 12187.
The general consensus is that the game needs to be installed and patched under Windows (http://www.planettr.com/forums/showthread.php?t=3889) but can then be run through Wine with the /NoPatch switch to skip the .NET based patcher.
However, a Linux launcher/patcher has just been released by a third party (http://www.lotrolinux.com/TR/) so it may be possible to install through Wine and patch with the custom launcher. I have used this launcher to launch the game, but as there has not yet been a new TR patch since the release of this launcher I've not yet tested the patching.
Having said all that, for the testing of the splash screen bug it may not be necessary to actually patch the client to the latest version since the /NoPatch switch puts you straight in, although this changes the conditions due to differing versions.
As per the forum thread above, the game itself requires Mono for Windows installing under Wine and d3dx9_33.dll in Wine's c:\windows directory.
I will attempt a regression test between 0.9.57 and 0.9.58. It's not something I've done before, but the instructions you gave seem pretty comprehensive.