The parent is just failing to explain a more fully developed concept called the "urban revolution", which classically has 10 characteristics of which writing is one and not all of which need to be present [0].

This entire discussion stems from the fact that the word "civilization" is essentially defined to fit the societies people already consider civilizations. There are technologically, politically, and socially complex societies that aren't "civilizations". My recommendation is to avoid the word entirely. Trying to use it scientifically leads to confusion.

[0] https://en.wikipedia.org/wiki/Urban_revolution