I found a way to get around the bug, but it's not exactly obvious. You can change the resolution by running the setup application, which is a bit hidden. Here's how I got it to work:
1. Open the folder where the game is installed (probably something like C:\GOG Games\Tomb Raider 1+2+3\Tomb Raider 3 unless you've changed it)
2. Open a command prompt in that folder (in Windows 8: File -> Open command prompt)
3. Type this into the prompt and press Enter:
4. Select the resolution you want. Press OK and the game will launch. Just don't open the sunglasses menu or the game will crash. After this, you should be able to launch the game normally in the correct resolution.
thanks. maybe I can get the resolution in my disk TR2 to behave itself that way too. (The GOG one's music is still bugged.) Although in that one the cutscenes go out of sync and the background ambient sound mutes after a music track plays. better than looping music tracks but I don't like having the levels completely silent. Brings back bad memories of my bugged as hell sold-out edition of TR1.