Seeing as it's been a week and no one has suggested a better idea...
I doubt you'll be able to get it to run natively, although via Steam's Proton, I've heard of more success with Civ III running on Linux in recent years - but even though Android has roots in Linux, it's probably too far diverged by now for that to carry over.
Thus the outside chance that
might work is using a remote desktop software to access Civ, running on your PC back home, from your Android tablet while on vacations. I've been using
Splashtop for accessing my Mac Mini from my Windows laptop while out and about, since I prefer PC laptop hardware to Mac laptop hardware, and it works pretty well. They also have an Android version, which I haven't tried, but they offer a free trial, so there's not much downside in seeing if it works. And at least for the time being, they seem to be having a first-year sale at €12 per year.
Will Civ III work well with such a setup? It might; I've forgotten that I was remoted into my older Windows desktop from my Windows laptop (using Windows Remote Desktop), fired up Civ III, and not noticed that I was playing via remote desktop for a while. It probably wouldn't work for a fast-paced racing or shooter game, but for Civ... I wouldn't be surprised if it provides acceptable results.
Perhaps even more likely to work is
GeForce Now, which lists Android as a supported client platform. They have a free tier, which is ad-supported and limited to one hour, but should be enough to see if it plays Civ III acceptably and thus if it's worth paying for the non-free tier. Though it will only work if you own Civ III on Steam.