DR-DOS was the best back in those days
I was a kid and used it to improve Doom framerates considerably if memory serves me lol.
I'd be surprised if nmap is any use, I doubt this rig uses TCP/IP, that came later iirc - probably IPX? and I doubt it's a router, but maybe. my guess is it's a straight metal hub, and if it's anything like the few old systems I've "salvaged" it looks like cat5 on one end but the other ends have all manner of weird serial-type D connectors lol. I could never figure out how all the stuff I found went back together! I had a look at that dolphin pos linked above, looks too new?
I wonder if modern virtualisation setups like virtualbox can operate with a weirdo network stack like this may have - I don't have much experience with them outside of running windows on a linux box. That may provide an easy way to provide backup capability and future reliable server hardware for a minimal outlay if you can image the server disk without trouble.