Short answer:

How things are isn't how they've always been, nor how they necessarily had to have been. Beware overinterpreting contemporary circumstances.

Discussion:

Recall how the Romance of the Three Kingdoms begins:

話說天下大勢，分久必合，合久必分

"It is said of this world that anything long divided will surely unite, and anything long united will surely divide."

Or, as the scholar of early 20th century China C Martin Wilbur put it:

[C]entrifugal tendencies were always powerful, and the area we think of as China was divided for periods nearly as long as those in which it was united

Europe and China each have histories that include both unification and fracture, of Empires and barbarian conquests, of dynasties rising and falling. China hasn't always been unified, and Europe has been on occasion.

The Roman Empire, and for briefer periods the Holy Roman Empire and even Napoleon's Empire ruled much of Europe. And matched against the occasional Charlemagnes and Charles the Vs there are many more would be unifiers who were stopped short of their goal.

If you'd asked this question about the year 30 BCE you might ask "Why is China divided into the Northern Wei and Southern Sung while Europe is united under the Romans?"

Indeed, if you'd asked the question about China during the "Warlord era" of the 1920s, you'd see just splinters where the Qing Empire had been. Where there is today just one splinter left -- Taiwan-- there could equally easily have been a dozen. Think of what China looked like during the Taiping Rebellion, the 19th century's bloodiest war, the many imposed treaties which compromised Chinese sovereignty. China looked very much like a parallel to the Ottoman Empire, a premodern polity destined to fall apart, the fracture lines determined by imperial ambitions, local military cliques, religious and popular movements. After a rising Japan defeated China in 1895 and seized Taiwan and Korea, and goes on to create the puppet state of Manchukuo . . . it's not hard to imagine some other path for China in the 20th century that leaves the territories that had once been the Qing Empire scattered like those that had once been the Ottoman.

That China is what it is in 2020 is thus very much a matter of the history of the 20th century and the victory of the CCP -- both against the Nationalists and against various regional insurrections. Ask the question at some other time, in some other circumstances, and you'd find a fractured China.

Similarly, in the 20th century there are two hegemonies that had the aspiration and the potential to control all of Europe-- German fascism and Soviet Communism. That they _didn't_ achieve these aims does speak to one element present in Europe that has largely been absent in China; offshore powers that with a defined national interest in maintaining a balance of power in Europe-- first Britain, then later the United States. China generally hasn't a powerful nearby power with a continuing interest in the fracture of China. The term for this strategic dynamic in Europe is "offshore balancing" -- China has only very rarely had this kind of problem, but we can see in divided Korea just how it might have played out.

Had George Marshall and Harry Truman felt differently about Chiang Kai-Shek and the Nationalists, one could easily imagine a China that like Korea might remain divided up to the present. The United States had invested vast sums in the Nationalists, and Stalin was never more than lukewarm on Mao's CCP. The Communist victory in 1949 now looks like a "return to the norm" of a unified China, but in a slightly different circumstance it could equally easily be seen as a return to a norm of warring states.

Sources:

Roberts, J. A. G. “Warlordism in China.” Review of African Political Economy, no. 45/46, 1989, pp. 26–33.

C.Martin Wilbur "Military separatism and the process of reunification under the Nationalist regime" in China in Crisis Vol. I Book 1, University of Chicago Press, 1968

McClam, Reginald J. "Pax Britannica: Historical Perspective of Offshore Balancing" in Balancing on the Pivot: How China’s Rise and Offshore Balancing Affect Japan’s and India’s Roles as Balancers in the Twenty-First Century Air University Press, 2016, pp. 19–34

Jeans, Roger B. “United States Policy and the Chinese Third Force, 1949-1954.” Indian Journal of Asian Affairs, vol. 14, no. 1/2, 2001, pp. 1–14.

LIN, MAN-HOUNG. “Taiwan, Hong Kong, and the Pacific, 1895-1945.” Modern Asian Studies, vol. 44, no. 5, 2010, pp. 1053–1080.