Age of Empires 1 and Age of Empires 2 followed the conventions of the genre pioneered in "Warcraft" by Westwood. There instead of going through "four ages" you could "improve your main building" through "three stages", from a "village hall" to a "castle". And instead of "Civilizations" it had two fantasy races: the "humans" and the "orcs".

The gameplay of the Age of Empires franchise is not informed by historical data but is copypasta from a completely different title. The reason is the only part that does not break the 20-years-rule on this subreddit: The America-made game International Karate was accused of plagiarism of the previous Japanese title Taisen Karate Dou in 1986. Although the gameplay was completely indentical the American court has acquitted it's compatriots because of a different setting. That is what stopped the arcade game era and opened the floodgates for genre gaming, for different companies refurnishing old titles with several superficial improvements.

The era movement is a convention of the "real time strategy genre". The units avaible throughout the different ages are, of course, completely wrong. It didn't take an advance from "the dark age" to "the feudal age" to stop using maces and start using spears. And the horse collar has been around for much longer than the middle ages.