Aziz pointed me to this article in Forbes, The New Great Game, which highlights the imperial aspect of the contemporary Chinese regime. It is important to emphasize that there is a striking disjunction between the manner in which the present spatial expanse of the Chinese state emerged, and the fiction which the modern Chinese state promotes to its citizens and abroad. The acquisitions which pushed China to the furthest extent in its history were achieved under the Qinq Dynasty in the 18th century. The Qing are also know as the Manchu dynasty, a pointer to the fact that they were outsiders. The Manchu elite took over the administrative apparatus of the previous Ming dynasty by the 17th century, but they were never wholly Chinese. The reality was that for much of the Qing dynasty China was part of the Manchu Empire. Though exemplary students of Chinese forms in their roles as Emperors of China, the Manchu rulers also remained warlords of the Manchu people, and it is in this capacity (albeit leveraging the resources of China proper) that they conquered the western territories, or pushed beyond Amur river to the north of Manchuria.
To the left is an image which shows the geographical expanses of the major Chinese dynasties over time (earliest to left, the last bottom right). Only one dynasty rivals the Manchus in terms of the territory which they controlled, the Yuan, the Mongol dynasty. Like the Manchus the Mongols ruled China as part of a greater set of domains. Of the remaining the dynasties only the Tang had a robust and wide presence in Central Asia, but this hegemony evaporated by the second half of the Tang.
Turkestan, Tibet and the lands to the north of the Amur (which were later extracted from the Manchu Empire by the Czars) were acquired due to the Manchu’s greater cultural and geographic horizons than the Chinese (or, more accurately, a syngery between the enterprise of the nomad and the economic base of the Han Chinese). Like the Mongols the Manchus had a relatively good relationship with the lamas of Tibetan Buddhism, and the acquisition of Tibet occurred by way of their conflicts with the western Mongols (Oirat). The conquest of Xinjiang occurred as a byproduct of the Manchu involvement in intra-Mongol politics, as the Muslims of the Tarim Basin were chafing under the hegemony of the Dzungar Mongol confederacy. The drive to the north of the Amur would be a natural necessity to buffer the Manchu homeland against the expansion of the Russians into Siberia. Native Chinese dynasties, such as the Ming and Han, were hampered in their forays out of China proper due to their inability to maintain supply lines indefinitely and inflict any final defeat on nomadic populations which coul take advantage of the strategic depth offered by their vast ranges. It is notable that the Chinese dynasty which rivaled, though did not equal, the Manchu achievement in Central Asia were the Tang, of partial nomad background.
The fact that China was part of a Manchu Empire mattered in concrete terms because many of the domains outside of China were administered separately (though later in the 19th century there was a trend toward more thorough integration as part of a modernization drive). The Turks of Xinjiang naturally would not consider themselves Chinese, since China was simply a subcomponent of a set of territories of which also included the city-states of the Tarim Basin. Similarly, the integration of Tibet into the Manchu Empire was cemented by the personal relationship between the lamas and the ruling Manchu, as well as religious affinities between the two peoples. China was a third party actor.
All this makes more sense if you keep in mind the personal aspect of rule of hereditary kingdoms before the rise of the nation-state. George III, the king against who the American colonies revolted, was king of England, Wales and Scotland, Great Britain, as well as Ireland, the United Kingdom. Additionally, he was the Elector of Hanover. The fact that Hanover and the United Kingdom had the same ruler did not mean that these two administrative units were fused, on the contrary one of the concerns of the bureaucratic and aristocratic classes of both domains was that they not become excessively entangled in the international or domestic concerns of the other (the creation of Great Britain was favored by Scotland’s ruling classes because they were excluded from many of the English colonies!). In 1837 Hanover’s personal union with the United Kingdom ended because of the Salian law of inheritance of the throne. Now the connection between these two regions is simply a historical coincidence.
Now imagine if England made a claim on Hanover based on the century of personal union between the two polities. This would be ludicrous. But in The New Chinese Empire the author recounts that several times during diplomatic visits by Russians Deng Xiaoping referred to the territories beyond the Amur which were lost in the 19th century as if they naturally belonged to the modern Chinese state. The reality of course is that these were conquests by the Manchus, and they were losses by the Manchus (though by the latter period the Manchus were far more Sinicized than they had been in the 17th century). For nationalistic and ideological reasons the Communist regime simply pretends as if the era of the Manchus was one where their domains were conceived of as a nation-state. Because the Chinese Empire entered onto the world stage in the 19th century in the post-Westphalian context the qualitatively non-Chinese aspects of rule in Xinjiang, Tibet or Manchuria were elided in terms of their relations with other states.
Most Uighurs naturally are ignorant of these details of history. But these details of history have no doubt shaped the attitudes of ethnic minorities like Uighurs and Tibetans, for their integration into the Chinese state is naturally a thin veneer because it is a novel and new aspect to their experience. China proper emerged in its present form in larg part because of 2,000 years of institutional governance modeled on the precedents set forth in the Han dynasty; most of the Manchu acquisitions naturally lacked this background. The attempt to centralize the Manchu adminstrative apparatus in the 19th century was stillborn because of the death spiral of the dynasty. Only with the rise of the Communists did the Far West became an integral part of the nation.
Note: China is a geographically diverse, but an ethnically homogeneous, “empire.” In the Soviet Union Russians were only ~50% of the population, while in China the Han are ~90%.