Quote from the release notes: "- Linux platform is supported now. The port is based on Wine with CSMT and PhysX hardware support patches enabled. "
That doesn't really help :) I know it's using Wine.
Downloaded it and tested. Basically inside the game's "game" folder there are 2 folders named "Game" which contains the TW game data and "Wine" which contains 300mb worth of wine files. There are also 3 scripts (created by the developer not GOG) named "RunGame", "RunSoundConfig" and "RunWinetricks".
Despite all this, it doesn't work the same way "click start.sh and run" as other GOG wine-wrapped games do, as you still have to install Wine for your distribution (also stated on the game's page).
Beyond examining the scripts and the folder structure I can't test the game any further than this as I normally run Wine in a very portable way but my guess is this: The configuration and the hard work is already done, your distribution's Wine package is the required spark to light the fuse.