Nobles are not necessarily involved with the military or religion.
Name one culture where the basis of nobility was neither religious nor military, nor derived from having religious or military ancestry. Because I love to study cultures and I've studied a great many cultures, but that one you name would be the most unique and interesting one I'd ever studied - being as it were so wholly unlike all the other ones.
Sure, fantasy in general is for the most part based on medieval England...
What? Did I say anything about making everything like Medieval England? Heck, my own biweekly D&D game owes far more to a fantasy India in a lot of ways than to medieval England. Or Ancient Egypt. Or medieval Thailand. Or medieval Tibet. England is pretty far down the list. Tonight's game owed more to the Mayans and the Mauri than medieval England.
...but in many parts of the world nobles didn't fight.
Let's pick Ancient Egypt. The two ruling classes where the Priests and the Warriors. The Pharaoh was worshipped as a living God, and was expected to demonstrate his power and authority by directly commanding his troops in battle. When a particular dynasty ended, the new Pharaoh was almost always one of the main generals and often also a powerful member of the priestly class.
What about India. In India, the ruling class was the priestly Brahmin caste that oversaw all religious duties. The next most important caste was the warrior class. The middle class of society was made up of things like temple singers, temple musicians, weapon smiths, and horse breeders that served the two ruling castes.
What about Tibet. The ruling class was monastic priests.
Japan. The ruling class were the Samurai or knights.
Ancient Greece. The ruling class was the independent farmers serving underneath a King who was both a constitutional monarch and served as High Priest, and the independent farmers or manor owners were not coincidentally also a knightly caste of heavily armored warriors who station was owed to the fact that they could afford to arm themselves with the then state of the art weapons technology. And incidentally, each manor owner also served as high priest over his household in charge of religious duties. The word 'aristocracy' is Greek for the caste of persons expected to serve as front line troops.
China. All those nobles in the Wu, the Jin, the Han, and so on and so forth battling for supremacy? They might not all have been military, but they were all of the military caste and their power was owed to their ability to project military power.
The universality of this can be seen by just how widespread and numerous the cultures were - from the Philippines to as you say Medieval England and everywhere in between - where the symbolic authority of the nobility was a sword.
You don't see a noble class whose primary duties aren't religious or combat until the rise of absolute monarchies and conscription in the West, and even then families involved were largely heirs of the knightly caste and were still expected - especially among the lower ranks of the nobility - to obtain commissions as officers and serve in the military (and to send younger sons into religious service). Indeed, that practice couldn't be said to really fall by the wayside until WWI cut down the gentry across Europe, but even so you still see the Prince of Wales in the military way way past medieval Europe.
We just have to ask ourselves if that's how dwarves organize their societies or if it should be procedural or based on religion or ethics or whatever.
I'm saying that an aristocratic class does not arise in a society unless in some fashion that aristocratic class is perceived by the society as providing protection for the rest of society, whether spiritual or physical or more usually both. So dwarf nobility might be based on martial process, or religious ceremony, or magical prowess, but its going to be based on something. Even if after 1000's of years pass, the nobility as it exists manages to become a leisure class that pays a subservient military caste, quite logically that's not going to happen in an Age where megabeasts are still running around. But even when that happens, almost as soon as it happens, what tends to happen is the authority of the nobility is usurped. If the aristocracy can no longer be looked to provide security, because Urist McFrontiersman with a rifle is every bit as good of a solider or better than Urist McArmoredKnight, then the aristocracy is stripped of its authority by Urist McFrontiersman or else Urist McFrontiersman kills off the old aristocracy and sets up a new order. That's happened countless times across countless human cultures in countless periods. At its very basic, that evolutionary fitness. Those that can't fight the wars give way to those that can.
You can't hunt animals to extinction.
Technically, that would only be true if there are at least some animals in the game flagged 'uncountable'. There are only a few 100 creatures in the game though, so if you kept your fortress going for a few centuries you'd extinct them all. Indeed, I know enough about the game to know that the extinction of mega-beasts not merely locally but globally is built into the game and accounted for.
But I really don't care that I can't hunt [all] 'animals' to extinction. I see no reason why I should hunt any one animal to extinction locally if that animal is globally present and has a high birth rate.