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There are several theories of disappearance of the Dorset people. Two are discussed in the article "Disappearance of Dorset Culture" published on the webpage of the Canadian Museum of History:
In the centuries around A.D. 1000, the Arctic climate was becoming significantly warmer than it had been since the development of the Dorset culture. Warmer summers would have produced changes in the movements of the animals on which Dorset hunters depended, and there must have been rapid and unexpected shifts in the amount and distribution of sea ice and open water. Disruptions in their usual patterns of hunting and travel must have created hardship, and even distress, for many of the small Dorset communities of the Arctic world.
The Inuit brought with them from Alaska the tools and weapons of a sophisticated maritime hunting culture that had developed in the rich waters of the Bering Sea. Capable of hunting animals as large as the bowhead whale, the largest creature in the Arctic seas, the Inuit could support much larger communities than was possible for the Dorset people. These communities were extremely mobile, travelling during the summer in large skin-covered boats ten metres or more in length, and in winter by sleds pulled by teams of well-fed dogs. The Inuit had little trouble expanding rapidly throughout the Arctic world, and as part of this process the Dorset way of life disappeared.
Remark. Inuit had some Mongol weaponry, so if they indeed were to fight the Dorset people, the latter would not stand a chance. Regarding Mongol weaponry (the bow), see for instance the book "Ancient People of the Arctic," by Robert McGhee, p. 226. He also describes one piece of archeological evidence supporting the invasion theory, namely the "Brooman Point encounter," more precisely, a violent takeover of a Dorset settlement by Inuits.
The Dorset people vanish from the archaeological record at some time between about A.D. 1200 and 1500. Their disappearance is best explained in the historical traditions of the Inuit, whose ancestors observed the final generations of the Palaeo-Eskimos:
"The Tunit were strong people, but timid and easily put to flight. Nothing is told of their lust to kill."
Netsilik Inuit, 1923
"The Tunit were a strong people, and yet they were driven from their villages by others who were more numerous, by many people of great ancestors; but so greatly did they love their country, that when they were leaving Uglit, there was a man who, out of desperate love for his village, harpooned the rocks and made the stones fly about like bits of ice."
Ivaluardjuk, Igloolik, 1922
In fact, genetic analysis shows that all Paleo-Eskimos shared the same mitochondrial DNA, which is passed from mothers to children. This unusual h*m*geneity suggests few women were among the early Paleo-Eskimo settlers, Willerslev says.
(The quote is from the article by Jia You, "The strange history of the North American Arctic", Science, Aug. 28, 2014.)
The more detailed paper is by Robert W. Park, "Stories of Arctic colonization", Science, Aug. 29, 2014, is behind the paywall.