These are all excellent concepts!
Another possible non-magical but still fantasy-like power source is actually burden animals. Maybe a couple of enslaved giant creatures can pull the subway. That of course will carry the complications of possible moral judgment over those who chose to operate the system this way.
Yeah, I thought of that, but thought for the fantasy mystery feel that seemed implied that this was not in the spirit of the question. There are actual example from history where this was done. Derinkuyu had stables and very likely used animals to move goods around.
Znojmo Catacombs (iin what is now the Czech Republic, labyrinth of 27 kilometers of under city tunnels) and Chelm Chalk (poland) while mainly used for refuges and goods during sieges likely used animals. But since not primiarly for transportation, they don't really fit the "subway" comparison.
Secret tunnels under Lyon, France were uses by merchants to move goods more efficiently, protected from the weather.
Horse or oxen powered capstans and funicular railways may be a better example. There are example of such systems used to lift heavy loads and power cable systems. Often these are gravity "railroads" with animal power used for the return.
For a fantasy system built by dwarfs just up the complexity and expand the areas covered and use cases. It might not be practical in real world applications but technically advanced, subterranean people with centuries or millennia living and mining mostly underground would have more incentives to do more with such technology than real-life humans ever needed (especially if you take slavery out of the equation).
But I also think that steam power and more anachronistic technology, would work. In the real world we have examples of marvels of civil engineer accomplished in the ancient world that were either forgotten or abandoned due to a variety of social causes (roman concrete, greek fire, the Antikythera Mechanism, damascus steel, Peruvian hydraulic engineering, Roman aqueduct technology, etc.
One fun thing I came accross was Vitrum Flexile (flexible glass). While just a legend or at best an exaggeration. I mean, we didn't have anything close to this until the 2000s. Willow glass comes the closest and the chemical strengthening, ion-exchange process wouldn't have been possible in Roman times. But I've always liked the legend and have though of building an adventure around it. But I would have some transmutation magic involved. A mix of pure physical science with scientific application of magic.