Does a portable version exist in nature?
At work, there's a ban on installing games, but it would be much more enjoyable to pass the time away from work with my favorite Heroes 3.

If the tablet runs on Windows, there shouldn't be any problems with the regular version. Just copy it and play. You might only need a connected mouse (or maybe you can play without it). I installed and played not only Heroes 3, but also Heroes 5 on a tablet.
Yes, if the ban at work is on creating games on the hard drive, then Menta's advice about a flash drive is absolutely correct. The game runs and works perfectly when it's entirely on a flash drive. (Even if you put it on a CD, it will work, but it will be difficult to create save files).