I'm not so sure about the last two...
Dwarf: standard mountain dwarf
Dwarrow: wilder hill dwarves (closer to the earth? gypsy magic?)
Deurgar: there should be some kinda evil dwarf race (white skin and black beard?)
Demiurg: some kinda forigner Indian-looking race (the sikhs have nice beards)
The Dwarrow should be the Dwarves that just don't live in a proper mountain biomes. They build their settlements out in the hills, plains, forests, swamps and deserts, Humie cities, whatever. Crusty, shitkicking, rebellious, rural farmer types. They are at home wherever a pickaxe can turn the earth and are satisfied with the fruits of the labor their calloused hands produce from the soil or bedrock... Their labor and their work assures their prosperity no matter where they strike the earth. (So wondering gypsy/ viking nomad types, yeah, just that they carve out proper bedrooms and stockpiles wherever they decicde to settle for the next few decades.)
Deurgar: they could be something like the "Deep Dwarves" or "Dark Dwarves" that are popular round here and have completely adapted to a very hostile enviroment deep underground. They worship demons and gods of wealth and military cunning. Pasty skinned, cave-adapted, dark beards and soul-less cataracts on their eyes that have typically seen nothing but "darkvision/ infrared" all of their lives. Perhaps they are the forgotten ancestors of teams sent into the seemingly bottomless pits sent to bring gold and wealth to their mountainhomes but were never to be heard from again. With this mission in mind, the dwarves dug into the riches of the underworld and produced, but with no contact with the world besides the hellish residents of their current abode they adopted a militarist and smash-first-eat-later culture not unknown in traditional dorfen circles, In the lightless, evil enviroment these dwarves have trained their senses and minds to deal with horrors and sensory deprivation completely alien to other dwarves.
Demiurg: These are a subtype of enlightened and exceptional dwarves, mysteriously drawn from those dwarves in fey moods, or some say possessed by forces unknown. that live in the most isolated and hostile of lands. Perched high on the most isolated of mountain peaks or far within the interior of the barren glacier wastelands of the poles. They are a small faction of scattered dwarves, said to be sorcerers and possibly immortal dwarves. They speak in obscure or ancient toungues and weild magic without a second thought, they might wear the uniforms of the soldiers from ancient armies and the expeditions perished in their harsh environes or wear the artifacts of long-forgotten kings.... (These Dwarves might somehow draw mass migration into their hostile hellholes to create a settlement... for reasons unknown to all but them)
Or something. The Demiurg you outlined makes me think of the Afghan sorcerer or guide in the movie "The Objective" in that they live in the middle of nowhere in some cave, in terrifying/evil/ inhospitable biomes... not even a Dwarrow would consider settling in. Intentionally isolated and holding some contempt for the world they have traveled so far to escape so many decades ago.