Seems to start up OK here. Have you installed the bits correctly? The mod expands to a folder called Conquests. That corresponds with the folder called /Applications/Civ III Complete/Conquests Game Data/ on the Mac. So:
The stuff that's in the mod's Conquests/Conquests/ folder has to go into /Applications/Civ III Complete/Conquests Game Data/Conquests/
The stuff that's in the mod's Conquests/Scenarios/ folder has to go into /Applications/Civ III Complete/Conquests Game Data/Scenarios/