Most games these days don't support direct serial connections. You can't just connect 2 PC's together with a serial cable and expect to connect through a TCP/IP network. A ethernet network requires drivers and hardware/software that can produce an OSI model structure. In other words it's a lot more complex than a serial connection.
What you can do is:
Set up a real network with 2 network cards and a CROSSOVER cable. Then connect the PC's directly. If you want more than 2 PC's then your will need to get a hub/switch as well and use normal network cables instead of crossover.
If both PC's are running XP, you can connect them with a Firewire cable (must have the right connectors on each end) and set up network emulation through Firewire However, I don't reccomend firewire networks because I'm sure it sucks.
As far as serial connections being slow, that is not always true. As a matter of fact both USB (universal serial bus) and ethernet networks are serial. Old school serial ports are slow, but serial connections are often faster than a similiar parrallel due to the simplicity and effeciency. It all depends on how it's designed. Serial ATA is a perfect example that is designed to replace current ATA standards that are parallel and slower. Oh yeah, fiber optics are serial as well.