Quite simply put: Democracy, and subsequently Socialism/Communism.

Before the arrival of democracy, the "inter-dynasty" periods in China were dominated by more or less the same system as the dynasties themselves: absolute monarchies. Although dynasties were ruled by Emperors, while the inter-dynasty periods saw lesser kings or warlords, the idea was the same for all of them - governance was in the hands of an absolute monarch. The only difference in inter-dynasty periods was that there were multiple monarchs who had not yet unified all of China.

Democracy as a mode of governance had not taken root in much of the Far East prior to the arrival of westerners from Britain, Portugal, etc. With the arrival of western colonial powers came the advent of western thought, with liberalism and democracy being a part of that.

The idea of democracy taking center stage in China was one that was nearly nonexistent until the rise of Sun Zhong Shan (孫中山), or Sun Yat-sen. Widely revered as the founding father of Chinese democracy, Sun Zhong Shan's beliefs, and the larger Xinhai Revolution that he was a part of, were centered around democratic ideals and forever changed the way the Chinese people viewed governance. Furthermore, the majority population group of China - the Han people - were dominated by the imperialistic Manchurian minority during the final dynasty, the Qing. Rule by democracy obviously favored the larger Han population group over the other minorities in China - including the ruling Manchurians of the Qing Dynasty - and that could have been part of the reason democracy was so favorably received.

Democracy, unfortunately, arrived in China at the same time as the ambitious Yuan Shi Kai. Although the Xinhai Revolution was successful in toppling the Qing Dynasty, it was only possible with the help of Yuan Shi Kai, the commander of the formidable, western-trained Beiyang Army, who basically defected to the revolutionaries and helped them to force the abdication of the last Emperor of the Qing Dynasty in exchange for being made President of the new Republic of China.

The first national elections in 1913 led to the pro-democratic Kuomintang (KMT) - of which Sun Zhong Shan was one of the founders - winning by a large margin. The KMT wanted to install a cabinet system, with a Prime Minister to keep the President's powers in check. This didn't fly too well with Yuan Shi Kai, who begun cracking down on the KMT in the same year. In March, Song Jiao Ren, the premier candidate for Prime Minister, was shot by a lone gunman. In November, Sun Zhong Shan, seeing the situation of the KMT worsen, fled to Japan. In 1915, Yuan Shi Kai moved to found a new dynasty and make himself Emperor. This proved a disastrous move on his part, as the people had mobilized in force only 4 years prior to demolish the dynastic system in the Xinhai Revolution, and he received little to no support. Once-loyal supporters left his side, and his absolute control over the Beiyang Army fractured. One by one, his commanders broke free and formed their own factions, and entire provinces and their accompanying governors rose up in rebellion against him. This was probably the point where you could say China had fundamentally changed for good; Yuan Shi Kai's failure was the biggest example that the Chinese people would no longer stand for dynastic rule, Han, Manchu, or otherwise.

References:

• Lee, L.T. and Lee, H.G. eds., 2011. Sun Yat-Sen, Nanyang and the 1911 Revolution. Institute of Southeast Asian Studies.

• Sheridan, J.E., 1983. The warlord era: politics and militarism under the Peking government, 1916–28. The Cambridge History of China, 12, pp.1912-1949.

• Young, E.P., 1977. The presidency of Yuan Shih-kʻai: liberalism and dictatorship in early republican China. Univ of Michigan Pr.

• Schiffrin, H.Z., 1968. Sun Yat-sen and the Origins of the Chinese Revolution. University Of California Press; Berkeley.