MIDI has no sound on its own, so it depends on the thing playing it. Windows' MIDI synthesis might have gotten worse, or you remember it on the particular sound card you had with 9x.
What a good demo! Yeah, I think I has to do with "updated" MIDI synthesis logic. The issue involves some of the harmonies; on modern devices, they start but never stop, then begin to layer on top of themselves, making it a total cacophony haha.
Here's a video I found of one of my favorite games sounding completely different from how I remember it: https://www.youtube.com/watch?v=inn7IE6-wgY