I think it also depends on how we define Europe.In this closely related thread, Somes J summarizes the points exactly!
This in a nutshell is why European Domination has IMHO an 80% chance even with a POD as far back as 5000BC.
Would an empire with its capital in the Middle East count as Middle Eastern even if it controls Spain (e.g. the Rashidun Caliphate)?
What about a situation where Europe is divided into various states, but many of them see themselves as part of a cultural continuum with e.g. North Africa (like the Romans; a Roman Spaniard would have seen someone from Carthage or Antioch as much more akin than someone from Denmark or Germany)?
And so on and so forth.
The geographic divisions in the OP are more projecting back from this world than based strictly on geography. There are plentiful examples, some fairly long-lasting, that straddle those divides.