During the rule of Emperor Claudius, which was known for his military expeditions against the German tribes of the Chauci and Catti, the population of ancient Rome exceeded any city in the Roman Empire.
which was known for his military expeditions against the German tribes of the Chauci and Catti, the population of ancient Rome exceeded any
known for his military expeditions against the German tribes of the Chauci and Catti, the population of ancient Rome was exceeded by no other
known for his military expeditions against the German tribes of the Chauci and Catti, the population of ancient Rome exceeded that of any
known for his military expeditions against the German tribes of the Chauci and Catti, ancient Rome exceeded any
known for his military expeditions against the German tribes of the Chauci and Catti, the population of ancient Rome exceeded that of any other

Explanation
The original sentence draws an illogical comparison between “the population of ancient Rome” and “any city in the Roman Empire.” First of all, a population of one city can only be compared to the population of another city. Also, the second term of the comparison must refer to "any other city," since Rome was obviously also a city in the Roman Empire.

I have question about the explanation itself. Why is this not valid ... "The population of ancient Rome was more than any other city"? Isn't this ellipsis? Do I have to say "The population of ancient Rome was more than population of any other city"?

Technically, yes. You have multiple ways you could say this:

The population of ancient Rome was more than the population of any other city
The population of ancient Rome was more than that of any other city

That sort of thing - you either repeat "population" (which is generally less popular) or you can refer to "population" the second time via a pronoun (which happens more often). But, yes, you do actually have to spell out that you are comparing the population of one city to the population of another city. I know we don't do this in everyday spoken language... but we're actually grammatically incorrect when we don't include that second noun (or pronoun). This grammar stuff is annoying, huh?