Are you sure you're using the executable from Gamersgate? My Vanilla exe from Gamersgate has never worked in the 6 years I've had it on machines with XP, 7, & 8.1.
99.999% sure (never claim absolute certainty for anything!).
I haven't messed with the GG installation on the XP laptop, beyond the cosmetic mods I mentioned,
but GG have definitely changed and amended their Civ3Complete package over the years (or rather, Firaxis have). CFC-user Etain pointed me in the direction of GG, but he/she did say that when he/she got his/hers(?), there was no Vanilla .exe included at all. So it's quite possible that my GG-version of the exe is slightly different from your GG-version.
In any event, has your XP machine installed the KB3086255 Security Update? If not, then that may be what is allowing that machine to play the Vanilla exe.
I just checked, and Vanilla does still run on the laptop. So if it is that update affecting it in Win8.1, then it hasn't been applied to my XP-install yet (and I do usually apply any security updates that the laptop asks for!). Which would kind of make sense, since M$ had already long since discontinued official support for XP when that update was released.
*I kid about playing Vanilla, but unless I'm mistaken all those issues you point to are not a problem in PTW, which is a far superior version of the game.*
Yeah, I know that. Problem is,
neither of my current GG-installations actually include a Civ3X.exe, working or non-working (AFAICT, only the executable is missing -- all the other PtW-content is there, including the Editor!

). Did/does yours?
If so, then perhaps after you DL'd it, and after GameSpy went defunct, some bean-counter decided that there was no point including the 'intermediate' version of multiplayer-CivIII, and ripped it out. Now that online MP-play is back via Steam, I'm actually slightly curious as to whether GG has also updated their download-package yet again, to (re?)include the Civ3X.exe -- their current advertising blurb certainly claims so, but then again, that was also the case when I bought it last year -- but I'm not curious
enough to want to reinstall the game with the Steam client attached...
Hence my interest in being able to try out the PtW-like Vanilla mod that was put together for the GotMs way back in 2002, while people were still waiting for PtW to become available in their sales region. I can certainly DL it to the laptop, but I rather wanted it on the Win8.1 box -- which means the NoCD patch is probably the best way to go...