I did this on the latest Steam version, but it may work on the GOG one:

- Run the game exe in Windows XP (SP2) compatability mode (none of the other compatability options were required for me)
- Open up QuickTime player, go to Preferences > QuickTime Preferences > Advanced and uncheck the three DirectX check boxes.

After doing this I got both the starting videos and New Game video to work.

Hope this helps.