There is nothing from the game causing the incompatibility, that is all from the installer.
I do not know why; it could be GOG's 2.8 is after a similar version or that it is just looking in the wrong place. Either way, GOG should not have released the game without testing it first, so this really should be sorted soon.
EDIT::
The game is fine, as I thought it is looking for the 2.8 version. GOG have silently updated the original Democracy 3 games to 2.8 as well (I had an e-mail this morning).
You only need to redownload Democracy 3's main installer and reinstall the game.
You will loose all of your save games and relevant unlocks.
Social Engineering and Extremism DLC's as well as any extra supplements you have also installed appear to carry over without any issues, but you might want to update them too anyway.