So the 3D in-game graphics are fine, but the videos and menus show this glitch. Maybe it is connected to video codecs. If you've got any codec packs installed, uninstall them and re-install the game. GOG support suggests to only install the
Combined Community Codec Pack (CCCP) if there are video glitches.
Sometimes there are problems with ffdshow filters. Here's what GOG support suggests according to this:
If you're using ffdshow (which is included in pretty much every codec pack), try adding add the game's executable to ffdshow's exclusions list - first in just the Video decoder, then, if that doesn't help, the Audio decoder as well.
To do this, you will need to access ffdshow's settings. You should be able to find an appropriate link in your codec pack's Start Menu group. For instance, for CCCP it would be Start -> Programs -> Combined Community Codec Pack -> Filters -> FFDShow Video Decoder Configuration. You should find FFDShow Audio Decoder Configuration as well.
Once in the Video Decoder's settings, go into "DirectShow control" and find the "Don't use ffdshow in:" setting and make sure it's checked. Click on the "Edit" button in front of it, then click the "add" button and browse to the game's executable file in the game's folder.
Now launch the game and check if the problem persists. If it does, add the executable in the Audio Decoder Configuration as well. If none of them help, you should go back and remove the exceptions.