If you looked at some data, europe often had 1/3 the population of the world, so a correct proportion would be 12/35. I included egypt in the west, so it would have been 16/35. If they included 10 more chinese leaders (kind of boring), it would have been 16/45, which is correct by population.
There are arguments for western bias, but your simple criteria isn't very convincing.
In terms of land, here's the list of the largest empires:
# British Empire - 36.6 million km²[1] (under King George V in 1921) (excludes Antarctic territorial claims)
# Mongol Empire - 33.2 million km²[1] (under Khublai Khan in 1279) (excludes Northern Siberia)
# Russian Empire - 22.8 million km²[2][3]) (under Nicholas II in 1895)
# Ottoman Empire - 19.9 million km² - (under Sokollu Mehmet Paşa in 1595)
# Spanish Empire - 19 million km²[1] (under King Charles III)
# Arab Empire - 13.2 million km²[1] (under the Umayyad Caliph Al-Walid I)
# Qing Empire - 12 million km²[4] (under Emperor Qianlong)
# French Empire - 11.2 million km²[5] (during World War I)
# Portuguese Empire - 10.4 million km²[1]
# American Empire - 10 million km² [6] (1898-1902 and 1906-1908)
# Brazilian Empire - 8.1 million km²[1] (under Dom Pedro II)
# Macedonian Empire - 7.61 million km² (under Alexander the Great)
# Achaemenid Persian Empire - 7.5 million km²[7] (under Darius)
# Sassanid Persian Empire - 7.47 million km²[2] (under Khosrau II)
# Japanese Empire - 7.4 million km²[1] (during World War II)
# Roman Empire - 6.5 million km²[1] (under Emperor Trajan)
# Ming Empire - 6.5 million km²[2]
# Han Empire - 6 million km²[2]
# Tang Empire - 5.4 million km²[2] (under Emperor Xuanzong of Tang)
# Maurya Empire - 5 million km²[2] (under Ashoka the Great)
All of them are in Civilization, except brazil (???) Chinese could use a few more emperors. And europe/america/brazil has 9/20 of them. china has 4.
Of the next twenty, there are some interesting ones left out: #21, Mexican empire. #22 byzantine (BTS), #23 Timurid Empire , #25 Hunnic Empire, #26 Seljuq Empire, #27 Seleucid Empire, #28 Italian Empire (Western bias), #29 Dutch Empire (BTS), #30 Nazi German Empire (germany), #33 Ghaznavid Empire, around Afghanistan, #36 Khazar Empire, Turkic, #37 Median Empire, ancient iranian, #39 Belgian Empire (western bias), #40 Inca Empire,
There were a ton of Indian empires, by the way, in there. Khmer does come later
By % of world population
1. Qing Empire - 36.6% (381 million out of 1041 million in 1820)[15]
2. Maurya Empire - 33.3% (50 million out of 150 million[25] in the 2nd century BC)
3. Arab Empire - 29.5% (62 million out of 210 million[25] in the 7th century)
4. Mughal Empire - 29.2% (175 million out of 600 million[26] in 1700)
5. Ming Empire - 28.8% (160 million out of 556.2 million in 1600)[15]
6. Achaemenid Persian Empire - 27.6% (42 million out of 152 million in the 4th century BC)[16]
7. Han Empire - 26.5% (59.6 million out of 226 million[15] in 2 AD)
8. Roman Empire - 26.5% (60 million out of 226 million[15] in the 1st century AD)
9. British Empire - 25.6% (458 million[27] out of 1,791 million[15] in 1913)
10. Mongol Empire - 25.6% (110 million out of 429 million[16] in the 13th century)
11. Song Empire - 22% (59 million out of 268 million in 1000)[15]
12. Spanish Empire - 12.3% (68.2 million out of 556 million[15] in the 17th century)
13. Russian Empire - 9.8% (176.4 million out of 1,791 million[15] in 1913)
14. Ottoman Empire - 7.1% (39 million out of 556 million[15] in the 17th century)
15. American Empire - 6.4% (146.4 million out of 2,295 million in 1938)
16. Japanese Empire - 5.9% (134.8 million out of 2,295 million[15] in 1938)
17. Vijayanagara Empire - 5.7% (25 million out of 438 million[15] in the 16th century)
18. French Empire - 4.9% (112.9 million out of 2,295 million in 1938)
19. Nazi German Empire - 3.3% (75.4 million out of 2,295 million in 1938)
20. Austro-Hungarian Empire - 2.8% (50.6 million out of 1,791 million in 1913)
21. Italian Empire - 2.3% (51.9 million out of 2,295 million in 1938)
22. Portuguese Empire - 0.8% (14.7 million out of 1,791 million in 1913)
What you can conclude is that Koreans, Aztecs, Mayans, Vikings, and Mali, are perhaps unfairly included to the detraction of Italian empires, austro-hungarian empire, and various Turkish and Indian and Chinese empires.
I had no presupposition initially whether your claim was true or not; I just realized there might be a critical flaw in it.