If you're already behind a router, then I wouldn't worry about it. Nothing can reach that PC unless it's in reply to a conversation that it started. Even if you install a local firewall, it's going to have to allow the same, otherwise the games wouldn't work. But still, a lightweight firewall won't add any noticeable load. Antivirus is what really slows down a computer, but if you don't mind it then go for it.
The only virus I've ever had came from me opening an insecure web server to the internet back around 2002 or so. That was an automated attack, but that was only possible because it was a server with a well known exploit, connected directly to the internet through a modem, and sitting there receiving requests from anybody. A game machine sitting behind a NAT router isn't going to have exposure except to whatever game server/peer it's playing games with. I suppose if the server was hostile and was programmed to utilize some known exploit in that game's networking, then it could be a risk. I think the odds are slim though.
To be really safe, you could firewall that PC so that it can't talk to the rest of your network, just the internet only. The most ideal way to accomplish that would be with an external firewall, not something that's installed on the machine in question. This does mean transferring files is sneakernet, though. In that case CDs would be safest, but regardless, make sure USB autorun is disabled completely on both ends (requires registry or poledit settings in XP, I don't know how it works in Win98).
I've thought about isolating an internet-only subnet for visitors using my wireless router. I trust my wired machines, but wireless == random friends/family with whatever viruses they've installed this month.