GG have definitely changed and amended their Civ3Complete package over the years (or rather, Firaxis have).
Mine's always been the same. It's always had the non-working Vanilla exe.
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 feel stupid now! You wouldn't have that security update because support for XP ended last April. THAT'S why it runs on your XP laptop. On your 8.1 machine just look up KB3086255 under "Installed Updates" and if it's there, that would be the reason it doesn't work.
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?
All the PTW content has to be there since it's needed for C3C to run, but I've also never had the Civilization3X exe as part of any Gamersgate downloads. I got my PTW No-CD patch from elsewhere.
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...
If I had to guess I'd say probably not. I, too, don't care enough to find out since everything is working perfectly now.