The only explanation I seen that is that some climate change that caused mass starvation. Do we have any evidence about what kind of climate change took place? Is there any other hypothesis about the demise of Dorset culture?
There was a recent study published this summer that sheds a bit of light on what happened (and what didn't happen) to them through DNA typification from bone and tooth samples from permafrost.
The results show that the Dorset were genetically distinct and did not intermarry with the Thuleans, remaining genetically isolated, despite the Thuleans arriving into Dorsetian territory at the onset of their decline. They also showed a considerable amount of inbreeding within the Dorset people, not exactly surprising, but it suggests that a lack of genetic diversity might have also left them vulnerable to exposure to newly introduced pathogens.
Where does that leave us for hypotheses then?
1 - They may have been wiped out by pathogens introduced by the Thulean which migrated into Dorset territory at about the same time they began a sharp decline. This might perhaps be testable through biocaracterisation of organic remains.
2 - The Dorsetians might have been outcompeted by the Thuleans for key resources. Hard to test directly, but a comparative study of the contents of middens on Thulean vs Dorsetians sites from the overlap period might be enlightening.
3 - The Dorsetians may have been exterminated by the Thuleans (see, for instance, the opinion of Fitzhugh), although that would be in contradiction with Inuit oral tradition which emphasises the gentle caracter of the Dorset people and insofar as Inuit oral tradition seems to be surprisingly reliable.
4 - Inuit oral tradition describes the Dorsetians as technologically primitive and shy, this might suggest rigid and aloof society refractory to technological change and vulnerable to change of any nature. And as you underlined, that period was one of climatic change (see: Little Ice age), where cultural rigidity might have been counter-adaptive, so that might have been a factor as well.
Note that these 4 hypotheses are not necessarily mutually exclusive, and that any of these factors may have contributed to the demise of the Dorset people.
If you're looking for a more thorough answer (really enjoyed the post and links from /u/Gargatua13013 !), I've been really impressed by Robert McGhee's work as an archaeologist for Parks Canada. He always publishes with a general audience in mind, and his use of archaeological evidence is clear and cogent. I read his Ancient People of the Arctic (1996) years ago, which would certainly be able to answer your question. But his most recent publication, The Last Imaginary Place: A Human History of the Arctic World (2007), looks like it might be an even better, more up-to-date reference.
I would, however, be wary of climate arguments. Since the late 1990s, archaeologists have been tremendously interested in climate, collected a lot of data, and really figured out how to use it really quite well. But if it looks like climate is the only explanation for a change, it probably means that the archaeologists weren't even looking for other types of evidence. That could be a funding issue: sometimes archaeologists get funded to research a narrow question, so they can only look at a single factor, such as climate change. As these site reports get compiled into longer narratives about the rise and fall of a culture, scholars sometimes lose sight of just how narrow their evidence base might be. Read with a careful eye! Good luck!
The theory is that the Dorset culture was under two threats.
The Alutes (our Inuit) were smaller and had a more advanced technology (composite armor, they had the drill to help them make things).
The climate went through a whip-saw in the 1650's or so. There was a little Ice Age. Some think that was caused by Europeans spreading disaease and wiping out Native Americans, and by that reducing slash and burn.
Very quick summary.. I didn't look online for confirmation.