huntintx: If I could send an email and get my code within an hour or two, fine. Some people have been waiting weeks if not months. It's a stupid system.
It is definitely annoying, especially because GOG doesn't mention anywhere that that is how it works. You WILL get one, however... I got mine in only a few days. Just make sure you fill out the form properly (from the "support" section of the website) and that the email they send you does not get caught in your spam filter.
I'm not sure why there's such a weird system for getting a multiplayer key... perhaps GOG's licensing deal for the game means they need to distribute keys separately, or it could have something to do with GOG's DRM-free policy.
Anyway, since you already bought the game here, you may as well request the key, and you should get it in a few days. Also, this is the only game I know of on GOG with such a system; otherwise I can definitely recommend GOG for buying games.