Robosport in 1995 supported TCP/IP play out of the box, and was a fantastic game. Still is, actually!
What you may be able to do (I think there's a program already but it would be easy to write) is write a serial device handler which pretends to be serial.device, but actually connects via TCP/IP.
Of course in these days of broadband you can even just send UAE memory dumps to each other too.
I say, anyone for Lords of Chaos?