Thief: Gold setup was erroring at the very end with a failure to run 'RegSvr32' for a .dll that was already in my wine setup. It's a bogus error, but the installer deletes everything it just installed if you proceed after this error, so follow my instructions below if you hit this issue:

1. Run the installer from the Linux command line: $ wine ./setup_thief_gold.exe
2. When the installer pops up its error dialog stating there was an error registering a DLL (for me it was in50_32.dll), DO NOT CLICK on the Exit button. Go back to your shell and:
3. Hit CTRL-C to kill setup_thief_gold.exe
4. Verify in your $HOME/.wine/drive_c/Program Files (x86)/GOG.com/Thief Gold that all the game files are in there (THIEF.EXE, miss*.dml, etc.).
5. Now copy TFix_1.27.exe into the Thief install directory;
6. Again, from the shell, run $ wine ./TFix_1.27.exe (it may report an error at some point but it's harmless and TFix seemed to complete patching everything...)
7. Now launch Steam and manually add THIEF.EXE forcing use of Proton 7.0 and it should run just fine.

I've only gone through the tutorial level so far but it worked flawlessly; The Options and Audio test features worked fine.