So why are dwarves all the same? Most other fantasy races enjoy considerable variety between settings, but dwarves alone are, basically, a stereotype. Everywhere. Why?
Because dwarves are fucking awesome, that's why. They're technologically-advanced Scottish-Viking-Norse-German engineers who drink constantly and kill things with axes and hammers, the two manliest weapons outside of one's fists, and are made up of 50% liver, 50% muscle, 70% beard, and 30% bad math. The only way you can make that more awesome is if they were on fireall the time.
Fun fact: one of the weird things inhabiting the outer planes in Dungeons & Dragons is a race called the Azer, who are indeed dwarves made out of fire.
I think for the most part the trope title is referring to the fact that, inside a given setting, all the dwarves are nigh-identical (by tradition). They get a fair shake at differentiation between various settings, depending on which elements of "traditional" dwarves one feels like emphasizing, similar to elves.
It's difficult to change dwarves up much, because if you do, they don't really feel like dwarves anymore. I mean, what exactly are dwarves if you take their stereotypes away? At least if you dethrone and unstereotype elves, they still have their magic, immortality (or exceptionally long life), and pointed ears. Dwarves are pretty much defined by their stereotypical beards, alcoholism, and metallurgy. Take that away, and you basically just have a human.
Why does any trope hang together? Dwarfishness is dwarfishness because it feels 'right'. If they have any real logic, it's probably as an anodyne to the Functional Magic, whimsy and Suspension of Disbelief that riddle the rest of a typical Fantasy Kitchen Sink. Having a character (or characters) who insist on preferring "real" things like hard work, ordinary food and drink, family and loyalty helps keep the setting believable. I suppose even the beards qualify as a nod to realism in the age before shaving cream.
What do dwarves do for food? They are commonly depicted living underground without a hint of sunlight. No sunlight, no photosynthesis means no farming for food.
There are mushrooms in caves. They don't need sunlight to grow.
Why do you think they drink so heavily? Lots of calories in booze.
Many real-world humans live in cities that are either entirely paved over or, at best, could sustain five percent of their population on the arable land left available (which usually isn't farmed anyway.) I'd be more worried about where they get their vitamin D... but vitamins generally aren't a significant factor in fantasy settings.