When I was reading about the rise of Mesopotamian city states, it was mentioned that a written language was needed to organize a community with a population of more than 2,000.
Yet in pre-Columbian Americas, there stood the Aztec and Inca Empire, even though they didn't have written languages. And the population of Aztec cities could approach 200,000.
When we talk about the Aztec Empire or the Inca Empire, does the word "empire" has the same meaning as it is applied to the political entities in the old world, such as the Roman Empire, the Islamic Empire, etc.? One would think about not only the Emperor, but also the bureaucrats, taxation records, written laws, etc.
Without a written language, were Aztec and Inca simply alliances of tribes? And how could they manage a city of 200,000 without written records?
As for the Inca, you'll be interested in what are called khipu, a system of record keeping using large arrays of knots and strings. I've written about them a bit before here, and you can also check out some of Gary Urton's stuff on them here. The khipu that remain suggest the Inca Empire had a more thorough accounting record than most other global populations at the time.
I too would challenge that 200,000 benchmark claim, particularly given that it is in reference to Babylon's public works, and that it comes from a book whose first printing was 51 years ago. Sites like Caral in Peru were building large scale public works projects hundreds of years before Babylon became a city without even clear evidence of a "state," let alone a system of writing. Nearly every inch of habitable land in the Andes is covered in terraces, canals, and other systems, often on a scale seen nowhere else on earth. Yet only two societies (Inca and Wari empires) conclusively used khipu.
I'll let out many qualified Mesoamerican flairs address the greater point of your question, but first you'd need to show some evidence that this claim of needing written language to exceed 200,000 was in fact true.
It could just as well be the case that you just didn't see single settlements reach that size before the introduction of written language not because of some requirement for language but rather just because the population was simply not that big. That is, the number coinciding with written language could be ultimately coincidental, but not co-relational.
Do you have a record for the claim of 200,000? Not because I doubt that you read it. I don't doubt that. I just would like to see it myself.
OP, where did you hear that the Aztec and Inca did not have a written language? Both civilizations had writing and record-keeping. Unfortunately, invading Europeans destroyed much of those peoples' records and other cultural artifacts, but a few elements remain. If you'd like to learn more, I'd look up Marc Thouvenot's "Nahuatl Script" for the Aztecs and just about any text regarding Quipu for Incan record keeping.