You ask an interesting question, and the answer is, er, complicated.
If we just go by a dictionary definition, then let's go with the good old Oxford English Dictionary, which defines colonialism as
(n.) the policy or practice of acquiring full or partial political control over another country, occupying it with settlers, and exploiting it economically.
Which seems simple enough: conquer, settle, exploit. But wait, do we not actually define some entities as colonies that fail to fit one or more of those three requirements? Most European colonies in Africa involved little permanent settlement of white Europeans; similarly we could cite British India as a case where permanent settlement was limited. In these instances, colonial power was exercised through military power and control over institutions (both existing and newly-created), rather than the supplanting of the existing population. Some colonies were arguably not economically-motivated in nature, and maintained at the expense of the country holding them: the leased territories of Guangzhouwan, Port Arthur, and Weihaiwei served purely as naval bases; even today the UK has overseas possessions like Ascension, the Falklands, and the British Indian Ocean Territories whose principal functions are military force projection. And of course, what about Ireland, whose long-term subjection to English and later British rule did involve a number of economy-affecting policies such as the Plantations, but where overt extraction of resources was not necessarily the primary goal? Now, you can argue that colonialism isn't just another word for 'having colonies': you can, in essence, have colonies not based in colonialism. But perhaps the issue is that 'colonialism' has been defined too narrowly.
If you can have colonies without colonialism, can you have colonialism without colonies? For instance, Michael Hechter has argued that the English and to an extent Lowland Scots were involved in 'internal colonialism' within the British Isles through the suppression of Celtic culture in Ireland, Wales, the Scottish Highlands, and Cornwall. We don't consider the Scottish Highlands to be a colony of the Lowlands, or Wales to have been a colony of England, yet colonialism still serves as a valid frame of reference. As alluded to above of course, the notion of Ireland as a British/English colony, and the characterisation of British policy towards Ireland as 'colonialism', are arguably less controversial. So perhaps it is merely a matter of conventional classification: the entire contiguous United States east of the Appalachians is colonial territory per that OED definition above, yet we do not, conventionally, refer to it as such (for the most part).
I would argue, though, that we can and should take a relatively broad view of colonialism, not so much as a set of practices but rather as a discourse, and one which can take many specific forms depending on context. In broad terms, however, I would define colonialism as a discursive state in which one polity claims the authority to arbitrarily disregard or overrule the agency of another, typically on the basis of a presumed inherent superiority on the part of the acting polity. I distinguish this from imperialism in that I define that as being a discourse advocating the geographical extension of state power. There can, of course, be considerable overlap, but such overlap is not total. It is worth clarifying here that I am not using 'polity' synonymously with 'state', as there are both non- and sub-state structures of political organisation that can mark a community as a polity.
Most discussions of Qing colonialism don't concern the historically Han-majority regions of China proper, but they provide a useful point of reference by giving some context to how Qing historians discuss colonialism in general, and thus how applicable the concept would be to China. When historians of the Qing call it a 'colonial empire', they are almost invariably referring to the empire's practices in regions beyond China proper, in imperial frontier regions like Taiwan, Tibet, Mongolia, Xinjiang, and southwest China. Some of these regions were subject to settler-colonialism, Taiwan and Xinjiang most prominently; yet a number of these were, in a broader sense, colonised through political reorganisation. Mongolian tribes were partitioned and confined to designated pasturages, while Tibetan Buddhism (which was also practiced by the Mongols) became integrated as a Qing state religion. Southwest China is a particularly interesting case because the discursive dimension is perhaps the best well-known, with Laura Hostetler's work examining how cartographic and ethnographic projects crystallised a Qing vision of what southwest China ought to look like, during a period (the latter half of the eighteenth century) when the actual extent of Qing power remained relatively constant. Of course, not all colonialism under the Qing was overtly state-sponsored. Much of the settler-colonialism that marked Qing policy in southwest China, Taiwan, and latterly Manchuria were the result of Han demands for access to land to which the Qing either acquiesced under pressure (Taiwan, Manchuria) or just didn't do much to stop it (SW China).
As such I think it makes sense to distinguish between three sorts of frontier colonialism under the Qing with somewhat different motivations and mechanics:
State-backed settler-colonialism, which happened in Xinjiang after 1828, Taiwan after 1862, and Manchuria after around 1850, involved the Qing actively supporting efforts by predominantly Han settlers to establish permanent settlements in the regions in question. The typical motivation was security, with the settler population(s) presumed to be more loyal to the Qing than the existing population(s) in the regions being colonised, and thus both directly and indirectly acting as means of heading off revolts and invasions. Security was not always the sole concern, however: while the sponsored colonisation of Manchuria was partially motivated by an escalation in Russian encroachments from Siberia, it was also prompted by economic collapse in the region, with the colonists being brought in to exploit previously-untapped arable land and mineral resources. In short, the Qing deliberately altered these regions on a demographic level in order to create an environment more conducive to their rule.
Institutional colonialism, which was the principal colonial mode in Tibet and Mongolia, involved the Qing emperors exercising an effectively unilateral claim to make changes to religious and political organisation, based on the either implicit or explicit claim that they knew what was best for them. In Mongolia this took the form of the jasak-banner system which delineated both the sizes and locations of tribal units, the subordination of Mongolian monasteries to the Dalai Lama-led Gelug priesthood at Lhasa, the replacement of Mongolian as a liturgical language in favour of Tibetan, and an attempt to create a unified, homogenised 'Mongolian' identity. In Tibet this manifested principally through the Qing essentially giving itself veto rights over new candidates for the Dalai Lama and other reincarnating clerics starting in 1792, an in the broader Tibetan world with the suppression of Bön and 'Red Hat' Buddhist sects in the aftermath of the Jinchuan Wars. In effect, the Qing relationship with Tibet involved a two-step process of strengthening the Gelug religious establishment's control over the broader Tibetan and Vajrayana worlds, while also strengthening Qing control over Gelug clergy and religious institutions. While institutional colonialism did not involve demographic alteration via migration, it still aimed at a similar goal of imposing a Qing-conceived order on a local population, dressed in some notional sense that the Qing were realising a Qing-created ideal cultural state for said populations.
Voluntary permanent migration, typically of Han Chinese populations, was sometimes resisted, sometimes ignored, and sometimes actively sponsored by the Qing, and applied to a number of areas including Southwest China, Manchuria before 1850ish, and can also be considered to include the emigrations that produced the Chinese diaspora in Southeast Asia. This can be considered colonialism in many instances where Han settlers outright displaced local populations, but it was not an inherently state-backed process, nor intended to strengthen state control. Indeed, at times migrants were seeking to move to regions where Qing control was weak or nonexistent. In these scenarios the principal motivation was the economic benefit to the individual migrant and/or households and social networks.