Good point. Still a little confusing how GOO works. So basically any game I buy that uses GOO as DRM will show in the client no matter where it is purchased from?

Because Steamworks is not a DRM, is intrusive as hell, and directly sends customer to a Steam, effectively serving as an in-built ad.
GOO is absolutely transparent; you can use GOO-protected product and know nothing about Impulse.
GOO ties your game not to internal Impulse ID, but to your email, AFAIR. If your email is the same for Impulse and GG, it should transport automatically.
Have you already started liking the GOO :-P?

If you already own it from Gamers Gate then you own two copies of the game. Do the right thing and tell them. Maybe you'll get something else you don't have. Or maybe not. I wouldn't use the free one if I already have a paid one though.
This couldn't be some sort of gifting misunderstanding, could it?

Or it could be Impulse GOO. Read up :p

I have no idea. It might depend on which GOO features the publisher enables or it might occur as a matter of course.

Retail CD keys for the following games will register with Impulse:
Stardock Titles:
1. Sins of a Solar Empire
2. Demigod
3. Galactic Civilizations Series (all of them)
4. The Political Machine (2004, 2008)
3rd Party Titles:
1. Red Faction Guerrilla
2. East India Company
3. Majesty 2