You could just share your Civ3 folder, but I don't think that it'll work, as it probably saves some values in the registry of the computer it's installed on. You'll also still need the CD on the computer you want to play on. It might also be that Civ3 installs some files other places than in the Civ3 dir. Games are notorious for putting stuff all over your computer, so I doubt it will work.
It doesn't matter if your network is wireless or not; as long as a program needs certain things to be present on the computer you play it on you can't run it from another computer which doesn't have those things installed. Of course you can try to track down every file and registry setting it needs and copy those to all computers on your network, but then there's loading times. A network is much slower than a computer, so it will take lots of time to load if you can get it to work.
That said, I'm not even sure if it will work even if you have all the stuff you need. But then I'm not a Civ3 expert, I'm just talking generally about how programs work.