Videogames rely on gameplay more than storytelling or teaching history. It's not a novel or encyclopedia entry. It's not unserious to expect a videogame to be fun over having a deep exploration over the possible interpretations of one word in its title.

Plus, some films are like Casablanca. Some are like History of the World Part 1. Additionally, if someone relies on media like Age of Empires, The Empire Strikes Back, or the novel Empire by Gore Vidal to gain an understanding of what an empire is, just because the word empire is in the title of these works, there are bigger issues at hand...

But the author, and it is quoted in the comment you answer to, say, explicitly "I bring this up not because I demand utter historical accuracy in my games".

The author, basically, says: I know games are not realistic, but the way AOE illustrates a misconception gives me an opportunity to talk about this misconception because too many people are still seriously believing it.

Of course, movies and games can take all the liberties they want, the author does not care about that. What the author raises is the fact that too many people still have an incorrect idea of what is an empire, and that this idea is a bit ridiculous when you look at the fact.

And it has current real consequences. For example, there are political parties that rely on such misconceptions to sell their fake news (edit: as illustrated below with someone commenting that the correct description of "empire" is the result of the author being "woke").