I like the idea of mining into the underworld itself. Maybe you need to divert the magma flow, not just bridge it, in order to drain the magma pocket and advance down more. In the game you could have several ways of doing this, including undermining the cap of the mountain and turning it into a volcano.
The Dark Lord I mentioned would be an eventual foe, like the Goblin King, and the Balrog. Mining too deep gets you material powers, but makes you risk the Balrog, but it makes fighting the Dark Lord easier if you win. And staying away from too deep makes fighting the Dark Lord harder than without adamantium, but without needing to kill the Demon you can throw your entire army into the effort to raid his fortress and take him down, and if you can waste him then smashing the Balrog shouldn't be that bad.
Basically, I'd make the demon a 'Boss' of a side-quest to unlock Mithril or Adamantium or something. If you choose to mine the SuperOre, you have to fight the Demon, but the SuperOre can be turned into anything and is just great at being armor and weapons, so it's really worth it. It's an 'advanced' gamer challenge suitable for the people who want to risk it for something big. Mining further down until you reach the underworld would be a similar challenge.
Then your Dwarf Lord could cease to be just Lord of the Fortress, but actually Lord of the Underworld. If we make the Underworld less about demons and more about, potentially, Dwarf Mythology then conquering the Underworld isn't an 'evil' thing, as it just transforms you into a Dwarf God.
Theoretically we could even make it so if you smash the Dark Lord's tower, you get a ring and could use that to become a Dark Lord yourself (which lets you start the game over, essentially, with goblins instead of Dwarves).
Instead of horses or mules, they could have ponies. A war pony is still a serious animal with training and power, but isn't the size of a full-scale horse. War Ponies could have a weight limitation on them to keep you from making them as powerful as a real horse when going into battle against knights (ponies are able to be ridden by children just fine, so a Dwarf wouldn't find problems with a good saddle), but once you get adamantium or the other super ores and are able to create Dwarven Metals (I'd make that a distinct subsection, and frankly, I'd rather make Adamantium something you add to an alloy rather than the super material itself. Let there be Mithril or Durmil or something and then that special stuff you add to it to amke it Adamantium) then you can make super-light armor and weapons and make armored Dwarf Riders that can go toe-to-toe with knights and break the point of mundane iron weapons easily.
They could also turn Elephants into Fortress Elephants, with massive arrow-towers on their back like people did to the large elephants in real life. Dwarves due to their size would even be better suited to this, as they could fit a lot of Dwarves on top of an elephant, and armor it with Adamantium eventually.