I have all the DLC and the game on my Steam account. It won't let me get my free GOG version.
I've got the exact same issue. I own 11 games on Steam from the latest Gog connect batch. The 10 other games have been added to my Gog.com account just fine, the problem is just with Democracy 3. :-(
I have contacted support and suggest you do the same to let them now it is not just one user having this problem.