I had problems running the game on Arch Linux. Running the game with "--log" created a log file in "/home/mjb/.local/share/doublefine/dott" with the following content:

Starting new log session.

Game: Unable to initialize FMOD: File not found. (iMUSEClientFMOD.cpp:586)
Game: Do you have 32 bit audio drivers installed? (iMUSEClientFMOD.cpp:589)

Ending log session.

I solved the problem by installing lib32-libpulse and lib32-alsa-plugins from the multilib repository.

Sorry to hear you had troubles and glad to hear that that error message was helpful (it was awkward to implement!).

For anybody who's not running pulse, relevant 32 bit Alsa libraries should also get you up and running.

Also relevant, somebody made an AUR package for the Humble version of DotT Remastered earlier today. I suspect that it could probably be adapted for the GOG version without much hassle.