Because we know the dates of certain aspects of those civilizations; when the pyramids were built, when the cities rose and fell in Mesopotamia, India, China, etc.
Since you disagree with the dating of the pyramids (at the very least), just ignore them and focus on the Tower of Babel. The date of the Tower of Babel comes from the Bible itself, as a certain number of generations after the flood. That is why the programmer who wrote this stopped the run after the date of the Tower of Babel. There was no way that the earth's population had gotten large enough for that incident to have occurred.
BTW, I do not use talkorigins as a "biblical text". It is a site that contains a large wealth of information, that's all.
I am given to understand the generations denoted in the biblical texts are not necessarily contiguous but general ascriptions so that we know the texts have a sound basis in history. Hence the dating of the Tower of Babel is subject to uncertainty, as is your friend's programming in relation to potential re-population.