I agree with the core of your post, but it should be noted that the great seas had been crossed for thousands of years at this time by Polynesian navigators (over the Pacific, not Atlantic), and had also been previously crossed by Vikings a few hundred years before.
The Aztecs had no written language equivalent to what we’re using here, and instead used ideographs. They did, however, record history cartographically!
Either way, it's a terrible definition. As an archaeologist, I use "prehistoric" to describe really old fossilized crap. Anything newer is historic.
My understanding - which may be wrong - is that it's at the level of much older high civilization. And I think that makes them "feel" as old as those civilizations, because we know so little.
I'm not sure the Aztecs were that technologically behind. The main reason they and all the other New World peoples lost was their less robust immune system. Typically, 80-90% of the population died of European diseases as soon as - or often even before - the Europeans arrived.
This was 300 years before germ theory, so no one on either side knew what was happening.
Does it? I always felt Columbus was pretty young history and I associate Aztecs with him. Not sure how the time period where we had guns and ships good enough to cross the great seas can be seen as super old, great civilizations had already existed thousands of years at that point.