Sweep of history games, such as Britannia and its spinoffs, History of the World, and others (Eurasia and Rise and Fall of Assyria are two of my prototypes), are never far from my mind. I have two all-of-Europe games as well, and have dabbled with several all-of-China games. (China's current boundaries, and Europe, are close to the same size.)
A problem in an all-of-Europe sweep of history game is keeping the small nations extant. Historically, small nations tend to hang around in Europe, complete with separate languages and sometimes separate cultures. The problem in a Chinese sweep of history game is that the dynasties dominated (at times), so getting rid of the chafe is necessary. The small nations can't be allowed to stick around TOO long.
And you could ask, why did China tend to be a universal state, while Europe did not? There are several reasons, such as the internal terrain, the external terrain and organized outside threats, culture, and language.
Mountain ranges and dense forest divided Europe into distinct geographical areas (the forest is gone now, but even in 10th-11th century Germany it was a barrier). The Baltic Sea and English Channel especially contributed to this division; we can also see the Mediterranean Sea as a separator with what might otherwise more sensibly be European North Africa than African North Africa. Then again, the Mediterranean can also act as a connector because it's a serene sea, easily sailed upon, compared with the northern seas. Further, owing to terrain and climate agricultural methods that worked in the lands bordering the Mediterranean did not work in northern Europe and vice versa.
The terrain within China is much less divisive than the terrain within Europe. The North China Agricultural Plain was the heart of early Chinese empires, with the addition later of the Yangtze agricultural plains. There is not quite anything like either of these areas in Europe, they are more reminiscent of Mesopotamia and the Egyptian Nile, where "universal empire" was common. These areas of China provided the basis for empire. Szechuan, which is separated from the rest of China by mountainous terrain, was sometimes a separate entity, and Tibet even more so, only recently incorporated into China. The southern half of China is more difficult terrain than the North, and was not incorporated into China until Roman times.
China is surrounded by difficult/unproductive terrain (steppes are agriculturally unproductive), even the sea is difficult because there's "nothing out there" (other than Japan, an unattractive volcanic stone backwater). Further, there is really no basis for large states in the areas adjacent to China. Japan is much too small, India is very strongly separated from China by the Himalayas, Southeast Asia is a jungle that supported only small empires, Tibet and the desert to the North could not support large numbers. The only real threat came from steppe barbarians to the north of China. And any time China was in good shape internally it was able to fight off barbarian threats, thanks to great superiority in numbers. China tended to self-destruct through overpopulation, but that’s a topic for another time: why empires fall.
Europe is surrounded by terrain that is sometimes easy to traverse. The near East provided a fertile ground for empires that could oppose a European empire, for example the Persians/Sassanids. There was still the pressure of steppe barbarians, and history shows them moving to the west more than they moved to the east. (Whether that was because there was less organized resistance to the west than to the east is open the question.) Perhaps it was harder to hold a "universal state" together in Europe against these outside pressures.
If North America had been occupied by Eurasian-like ancient-medieval cultures, it probably would not have been a single empire. The Great Plains, and then the Rocky Mountains, divide it strongly; the Appalachians would also have provided a strong barrier. On the other hand, there might have been no outside threat for a continent-occupying empire.
Here we might interject that pre-modern empires suffered from poor communications. If your emperor is 3,000 miles away, you're probably going to ignore him. One reason for the success of the Persian empire was efforts to establish good long-distance communication. Rome relied heavily on seaborne communication--it was essentially a Mediterranean empire. In other words, there were practical limitations to how large an empire could be, that were rarely overcome.
Psychological factors?
What about the mind? There is a tradition in China of the universal state, starting with the Shang and Zhou; even those "empires" were probably not empires in the sense we usually think, but Chinese thought of them as empires. There was only one "universal empire" in Europe, and it didn't occupy all of Europe, it was really a Mediterranean empire.
In China there is a language division between north and south, Mandarin and Cantonese, and there have been times when the two areas were separate empires, for example the Jin and Sung before the Mongols attacked.
But compared with Europe, this language divide is nothing. One can suppose that common language is one of the main ingredients that holds an empire together. Latin became the common language in the western Roman empire, though Greek predominated in the east; and in the end the West fell, while the east stood for another thousand years. On the other hand the Persian Empire was quite polyglot. Even when China was conquered by outsiders, they soon adopted Chinese language (and culture).
There was a tradition of empire in Europe after the fall of Rome, with Charlemagne crowned Emperor in 800 AD, and much later a "Holy Roman Empire" was established. But language differences, failures of technology, and the terrain generally mitigated against re-establishment of the Roman empire. On the other hand, the Byzantine Empire persisted for centuries, though at a much-reduced scope after 1071.
Culture (and language)
Culture, too, helps make empires homogeneous so that they can hold together. Chinese culture always predominates within China, especially in the minds of the Chinese, who think of the rest of the world as barbarians. There is not (and never has been) a single cultural tradition in Europe as strong as Chinese culture, though we owe a lot to the ancient Greeks. Perhaps if the Greeks had lived on a very large agricultural plain, their culture would have come to dominate a large area of Europe. As it was, divided up by the terrain of Greece, Greek culture was borrowed by others rather than dominating others. Hellenism was supreme in the Near East for quite a while, but even there it never filtered down to everyday folk.
Egypt and Mesopotamia benefited from common culture, as well.
Of course, the existence of an empire can spread what becomes a common culture and language, as happened with Rome.
Other empires
How about locations other than Europe and China? The Indian subcontinent, less than half the size of Europe or China but still half the size of the contiguous United States, has spawned many empires. But these empires ordinarily control the agricultural, lowland northern Ganges plain (much like the North China Plain), not the rougher, plateaued south or the mountainous west (Pakistan). India is more like China than Europe insofar as external threats, mostly former barbarians, came from only one direction, over the northwest mountains from Central Asia. Historically the Indians were controlled by foreigners more than the Chinese were, especially by Muslims such as the Mogul Empire. An Indian culture and language remained sufficiently diverse that it was not able to assimilate foreigners as rapidly as the more uniform Chinese culture.
If we look at the earlier and smaller empires of the Near East we see that they formed in areas with no terrain barriers, but were subject to barbarian incursions from many directions. The Hittites may be suggested as a terrain exception, but they had an awfully small empire. Though they once sacked Babylon the strain caused their empire to collapse. And unlike the larger and more stable empires of Mesopotamia and Egypt, the Hittite Empire was overwhelmed by barbarians in the near Eastern "Dark Age". The normal state of affairs in Mesopotamia was a universal empire, and the same can be said for Egypt. They were rarely both part of the same Empire because of the barriers of the Sinai and Arabian deserts.
The Mongols and Gokturks (Blue or Celestial Turks), among others, maintained generations-long empires in the steppes. Again, there were no internal terrain barriers to speak of, and little likelihood of incursions from outside. But failures of leadership usually led to disintegration of steppe empires. Agricultural empires can better cope with poor leadership.
