I think it’s just a game mechanic to show progress haha, considering that in the late stage most of nations/empires were in decline, not at their peak
Pollitically? Yes. Culturaly? No, they intermarried with the Spaniards and even today 1.5 million people speak Nautalh the native tongue of the Mexica people, thats more then any other North American language. The Mexicans/Spaniards took over a lot of Mexica traditions and still now things like The day of the dead have their origin from Native people.
In terms if the original cultute still exist, no that doesnt exist anymore, but many aspects survived into Mexican culture and ofcourse rituals where you sacrafise people isnt a thing anymore. But the culture wasnt just destroyed when the Spaniards came.
I would say a combination of both.
In campaigns “Ages” mostly represent “development level of your town/base” because very few campaigns lasted that long to cover different time periods.
E.g. Battle of Tours in AOE2 happened in the historical “Dark Age” but the scenario started in Imperial (which has a 15th century look).
But sometimes they also limit your maximal “development level” in many campaigns, mainly to avoid too anachronistic units like in Act I Blood and the AOE2 El Cid campaign (though they still cannot circumvent conquistadors).
In custom battles it feels like 50% “actual historical periods” + 50% “development level of your town/base” .
For Europeans that aligns a little better with progression in time, both by changes in aesthetics and technology (dragoons and cannons should exist in the historical “Colonial Age”, though, but that’s the “development level” side of thing). For Natives and Asians however most units just get a more elaborate look, but they still have some more “advanced” units unlocked.
If “Industrial Age” for Aztecs implies “what if Aztec reaches the Industrial Age” (like in Rise of Nations) they should have gunpowder and factories as well.