If the question is implying would he be better remembered by history, I think his being white would have made little difference.
Caesar is remembered, glorified even, because of his association with the rise of the Roman Empire, a leading force for civilization and a state which promoted laws and culture. While many people suffered under the Pax Romana, the point is that Rome was an empire which brought order (yes, at the point of a sword).
Alexander is also associated with civilization, he identified as Greek (he was after all a Macedonian) and introduced this culture to the lands he conquered. He wasn’t content on the culture he grew up with but instead wanted to fuse the cultures of Greece and Persia to come up with a hybrid; the best of both worlds. Alexander had the far seeing ambition for an empire which would stand the test of time (to borrow a line from the Civilization series).
In contrast, while Genghis Khan conquered a lot of territory (like Caesar and Alexander), he never founded an empire which effectively administered those territories. Genghis is not associated with laws or cities, taxes or culture.
The words of Caesar apply to Genghis, I came, I saw, I conquered. And really, Genghis’s legacy ends at “I conquered”, Caesar’s and Alexander’s does not.
Genghis’s descendants also carried on the family business of conquering but not building anything. His son, Ogodei rampaged as far as Korea and Russia but drank himself to death in 1241. Tamerlane sacked Delhi, crushed the Ottoman Turks at Ankara and cut a swath through Central Asia before embarking to conquer China, he died en route.
Some of Genghis’s descendants did manage to form empires but these are not known for their administrative durability.
The Mongols under Kublai Khan did conquer China and establish the Yuan dynasty. At the start of the dynasty China was administered as just another part of the Mongol empire but this was reversed in 1307 where China became the center of the empire and the Mongol steppes as mere adjuncts of China. Chinese culture won out over the invaders.
Batu, Genghis Khan’s grandson, conquered Russia and established the Khanate of the Golden Hoard in 1236. While the Golden Hoard was influential in its time, it’s ambitions were more concerned with exacting tribute from its Russian vassals.
Central Asia Timeline – Circa
North Asia Timeline – Circa
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