the ancient egyptian empire lasted over 3k years

No, not even close. The Egyptian Empire lasted from 1570 to 1069 BC.

The claim comes from John Glubb

No, there are others as I've already mentioned. The Changing World Order by Ray Dalio also arrives at the 250 year number. Cliodynamics and Structural-Demographic Theory suggests cycles of 200-300 years as well.