I do remember the game is 640x480 or something like that.
Today I play on 5120x1440. Is there any way to change the resolution to fullscreen on my monitor?
Maybe with NVidias image processing or something like that?

I doubt it is possible at the moment, unless it is a windows program, and somebody made a new wrapper for it. Which I doubt, since it is a fairly forgotten game.

But why would you even want to run a game like that in such a high resolution? To get everything to look as sharp as possible, or because you don't like pixels? Or because you don't like black bars?

A game made for 640x480 which would be run in such a high resolution, would make everything extremely tiny. You would lose a lot of the experience of immersing yourself into the game world by doing that, and it would probably also be much more difficult for you to see the details of the artwork in the game.

I don't think a tiny amount of sharpness or no black bars is worth that, but of course preferences vary a lot. It is very different with strategy games in 3D, where you can zoom in and look at the details when you want, and zoom out again for a greater overview. Something like that is generally not possible in old 2D strategy games, without losing a lot of immersion.