Is this a coincidence, or is there a clear historical differentiation that can be determined by geographical distance from where our species began?

I wouldn't draw the line that far back. But power does have a tendency to dissipate to the peripheries since urban civilization began in Mesopotamia around 3000 BC, for instance, the Greek cities was unified by Macedon, the Hellenistic era ended with the unification of the classical world by Rome, China was unified by the state of Qin, all of which were periphery powers, often thought of semi-barbarians, yet they ended up becoming the new center of power at the end of an era.

Ian Morris makes the argument that there is a certain advantage of backwardness, in which less developed regions benefit from being less advanced on the long run. For instance, in ancient times less advanced peoples often adopted innovations in weaponry faster because they don't have the deadweigh of institutional inertia more developed societies have: examples would include the relatively slow adoption of the chariot around 1700 BC by the western "core" in Mesopotamia and Egypt compared to other actors. The same might have being true of Mycenaean Greece w.r.t iron weapons and anti-chariot infantry tactics around 1200 BC. Another more recent example would be the rapid economic advance of East Asia due to its cheap labor: a function of its relative lack of development compare to the west. Those advantages means that often power starts to shift towards less developed regions: making those peripheries the new center of the "core".

I wouldn't call it determinism, but throughout history there is a tendency for development in the "core" to inadvertently benefit and draw in peoples or geographical areas in the periphery, eventually leading to power to be transferred towards the periphery. This is by no means an unbroken exception nor the only reason why say Canada has a higher gdp per capita than Iraq, but does outderly broad trends.