Answer:
I do not think world systems theory explains everything there is to know about the world. The very large cities, mega cities, those having over 10 million population, (a category including meta cities, over 20 million population, as these terms are not rigidly defined), rise up all over the world.
This article lists mega cities with current population estimates.
I do not know who is publishing about World Systems Theory and defining peripheral cities currently. I saw a map from 2000, 20 years ago, during which time China has grown enormously, industrializing, building a nationwide high speed rail network, and is now the nation using the most energy each year. It seems that the definition of periphery nations might need some revising.
It is logical that China and India with their large populations have megacities. And it is logical that other global cities are in that same class, like Tokyo, London, Paris, Buenos Aires, and New York City.
