Dark_art_: The only board-like game I seem to recall on GOG is
Trough the Ages, not cheap nor old but on my interest list.
That was my first thought as well, especially since it's on sale and on my wishlist, but it apparently does not support multi-player. Galaxy Trucker, by the same people, does, though, but I haven't looked at the multi-player aspect as I am not interested. Not in any way civ-like, though.
To the "Age of Civilizations" recommendation I'd add Alpha Centauri and Civilization 3, both of which are actually old and cheap here. None of these are really like board games, though.
I would not recommend AoW3 because it requires an account for on-line multi-player (and is impossible to reasonably use saves for PBEM), but AoW1-2 are fine. Also, I don't think SteamWorld Heist is multi-player.
While we're recommending free/open source games, I'll mention
triplea, a game originally based on my favorite board game of all time.