Could anybody pleasy tell me what kind of multiplayer Chaos Overlords supports? Local Multiplayer/Hotseat would be awesome...

I played this game in hotseat years ago, and I can confirm you it works in the gog version (just checked for you).
However I can't tell you how it works in a more remote fashion

Thank you. Hotseat is all I need.

I've never played this game on multiplayer before. How does it work?

Turn by turn. You play your turn, and then you wait for other players to make theirs. IIRC (it's been 10 years since I last played probably), you are sent to a lock screen where you can see other players' progress when it's not your turn.

Sounds cool. So, how do you get started?

I was wrong about it being a waiting. Everyone goes at the same time, and then when everyone's done, a new turn starts. I don't remember the menu selections to start multiplayer, but I do know it runs through TCP/IP where one person hosts and everyone else punches in the host's IP address. The problem is the game was created well before widespread use of routers, so you have to, first, get your external IP address (just google "my ip address") and then configure your router using port forwarding so that incoming queries are directed to the host's IP address. Here's some more detailed directions: http://www.computerhope.com/issues/ch001201.htm

Only the host computer has to do this. Everyone else should be fine if they just punch in the host's IP.

Yes, it is. And I did play it with two friends a few days ago and we did have a blast playing it ;) Highly recommended!