The only thing I got from that video that genuinely interested me was that Achaemenid Persia housed almost half of the world's population at the time.

Seriously?

Other than that, the idea of any of those contenders ruling (most of) the world for a meaningful period of time strikes me as far fetched. Having a large colonial empire is not necessarily a sign of great strenght, either - France and Britain had a hard time fighting Germany in World War I, in spite of their immense colonial possessions.