Believe the Gamespot review -- this was a weak effort.

User Rating: 4.7 | Civilization III: Play the World PC
Yes, you can play online. With some added civs, like, ummmm... the Koreans and Celts? Huh? I bought this because I thought playing online was the way to go. Well, maybe it is, but not with Civ III. It just never really took off. If you're looking to play via LAN or just play against your friend, this thing is sure to be heavily discounted (or unavailable), and worth your while. But to play competitively online, this game is worthless. Lag is always an issue, turns seem to take forever and your desire for fun will quickly turn into a desire to sleep or destroy your computer.