It crashes on my PC regardless of compatibly settings or admin settings and the fact that I am running it outside of the program folder. It crashes regardless and tells me that "GOG.com video player has stopped working."

Very strange :(

Launch the game from frontend.exe (in your Worms 2 installation path) instead of the GOG launcher.
You won't have the random video when launching the game, but you will be able to play.

You can play the video with any video player if you want to see them.
The game should launch first Intro.wmv, then a random video chosen from any of the other .wmv files.