How did a nomadic minority group the Manchus come to rule over China?

If they worked anything like the Mongols and other nomads that went imperial, they absorbed those they conquered, giving them a level of autonomy backed up with quick and brutal reprisals if they stepped so much as an inch out of line (and that could involve the sacking of cities, killing the entire adult population and selling the children into slavery in case of the Mongols). Do that a few times and an a population tends to get the message that they'd best do as they're told.
Also give them a decent living by not overtaxing them, probably taxing them less than their previous overlords used to do, and you've made a population that isn't likely to rebel, in fact will police itself against rebellion.

And as you said, being what they were they would have been very hard to fight effectively by the traditional means of Chinese armies (just as the field armies of the day in the middle east and Europe had no effective counter against the Mongol hordes until they themselves adopted large scale cavalry tactics, combined with firearms).

So study the Mongols as they swept out of the steppes to form an empire stretching from current day Mongolia to the gates of Constantinopel and beyond and you find pretty much how the Manchu could do the same in China (with the added advantage to them that the Chinese had a far more formalised and inflexible form of warfare established over more than a thousand years and were thus less prepared to deal with a radically different enemy than were the Europeans that eventually stopped the scourge from the steppes.

There was a "civil war" between two Chinese factions one under Wu Sangui, the other under Li Zicheng that handed the balance of power to the "Manchurians."

This occurred after the "Nuzhen" or "Jurchen" (Manchurian) tribes had been united under one banner, with their capital and Shenyang.

http://www.travelchinaguide.com/intro/history/qing.htm

A similar division of "China" between the Jin and Song dynasties accomanied by a similar unification of the Mongol tribes under Genghis Khan led to the Mongol conquest of China.

Put another way, the "stars aligned" for both the Mongols and the Manchus at different times.

By the name of Jurchen they were known for they high culture long ago. Tengis-Khan win over China, but did not win over this nation. Only his heir Ögedei Khan did manage it.

They already ruled China in the past - Jin Dynasty (1115–1234) in China. Sometimes, they were vassals of China. China, Korea, Manchu and Japan were all parts of one cultural space.

So, they were no insignificant, no hunters/gatherers, no nomads. And their winning over China in 16-17th century was a thing not a bit outstanding.

Perhaps part of your confusion stems from a misunderstanding of the Manchu. They were not, as you say hunter-gatherers. Rather, they were pastoralists. Hunter-gatherers, as you rightly point out, tend to have very low populations. They have to rely for sustinance only upon what nature has available where they happen to be living.

Pastoralists raise their own herd animals, which typically can subsist off off grasses. While this does require a great deal of mobility, if the terrain is right it allows a nation of pastoralists to have far more people than a hunter-gatherer socity.

Agricultural societies don't have the drawback of mobility, feed themseves directly (rather than indirectly through animals), and thus can achieve even greater populations. However, pastoralists still have one trump card that the other two types of societies can't match: It turns out that mobility is damn useful in warfare as well. Pastoralists have a lifetime of mounted training that residents of other societies have a hard time matching. This fact has always allowed pastoral societies to punch way above their population "weight class".

In China this meant continual conquests from the grassland areas to their north up until the modern age. This includes not just the Manchu but before them the Yuan, Jin, Former Qin, Northern Wei, Northern Zhou, Later Tang, Liao, and Xi Xia.

To begin with, the Empire was rocked with two major peasant rebellions at the same time as the Qing invasion - when the palace appeared as if they were going to be overrun by the newly declared Shun Emperor, the last emperor of the Ming dynasty, Chongzhen, went nuts and killed his entire family before hanging himself, leaving a succession crisis on top of everything else.

Meanwhile, the Jin dynasty had, at the time, consolidated politically, and developed a formidable army with the right combination of training, tactics and leadership to win major battles against a moribund and complacent Imperial army. They also had the political savvy to bring disaffected nobles and officials to their cause, most notably General Wu Sangui. With the defeat of the Shun Emperor at Shanhai Pass, the supremacy of the Qing was assured. It took a succession of emperors and a few decades before all of China was brought into the new empire, mostly due to resistance to being ruled by yet another outside power - but in the end, Hong Taiji was able to reconcile the culture of the Manchu with the culture of the Han, and cement the Qing as a dynasty.