I wouldn't call it a big intellectual problem for me, but it just seems curious - intuitively it would seem that the opposite should be the case. And indeed some games are working so fast on 20-years-later computers that they require special speed settings in Dosbox, but some things work surprisingly slow.
Disclaimer: I'm no "geek" or "nerd", so I hardly know anything about the phenomenon's technical basis.
Two examples:
1. "Leisure Suit Larry 3", the gym scene. Without debug mode on, it may require very high numbers of repetitions on each machine when playing on faster computers - I've read that someone actually tested it and these were numbers in the area of several hundreds...
2. Fast-moving objects in a few other games - I recall two examples from "Ecoquest 2". If you have played the game you probably recall the Ecorder, which Adam uses to record information about the environment. On the highest tree above the canopy there is a little bird which you can "catch" with the Ecorder and talk to it for a few points. Later a Morpho butterfly appears in the village, you have to catch it and give it to the shaman. I recall both the bird and the butterfly move extremely fast on my 90s computer - it was quite tricky to click in the right moment (the butterfly was less of a problem - it moved all the way to the left when Adam got the potion to lure it and you just had to use the Ecorder before putting the cup on the ground). On my current computer, which is probably over ten times faster - such objects are still quick, but it's completely possible to "catch" them, no frantic clicking all around. I'd say they seem about three times slower.
3. Examples which don't affect gameplay, but work the same way: sneaking from one obstacle to another in "Ecoquest 2" (Slaughter's camp) and "Pepper's Adventures in Time" (getting into Penn Mansion).
It seems quite counterintuitive, so why do faster computers seem to slow some things down?

I don't think that it's a case of a faster computer making for slower results so much as a case of different hardware timing producing different software timing, sometimes producing expected results (too fast to play!) and sometimes counterintuitive ones. I remember learning about this in Alone in the Dark 2 when apparently dodging the Poseidon-statue's thrown trident at the top of the stairs was only possible on certain Intel chipsets. Typically it results from programmers trying to directly anticipate likely timing values for the kinds of hardware that the average consumer will have at the time of the game's release rather than programming "for the ages" and writing a timing algorithm which will scale as hardware power increases -- see Trixter's trivia entry for Alley Cat for more on that bit.

Note how I'm not answering your question at all 8)

Pretty much the gist of it is imperfect programming; the game recognizes that it will need to slow itself down on faster computers, but the algorithm it uses to do so isn't written well. Whatever trick the game uses worked well on machines of the era, but overcompensates with machines faster than anything the developer imagined at the time.