For the past five centuries, European countries had explored and colonized the world. Today, European languages remain big lingua francas, most countries are former European colonies and Christianity has been spread by Europeans across the world. But is it possible for some other region of the world to dominate and colonize the world the same way Europe did? Which region is the most likely to do so and why?
I think it will pay to be specific here. Just some thoughts about what domination means, the concept of European domination, and the costs associated for both.
France, what became the UK, Spain, Portugal, and the Netherlands dominated the world. Russia certainly became a major player in European politics as well as Asia. The reach of Slovenia and even Belgium (despite its big slice of Africa) were nowhere near as wide-reaching as that. Hell, the British Empire's "domination" of the world was only a concrete fact from the 1840s to about the 1950's. Claiming dominion over wilderness and swathes of cultures that you couldn't do anything to or with until 200 years as passed is hardly domination.
Establish perimeters of what you mean by domination. The Spanish Empire was at the top of a convoluted power structure until it collapsed 400 years on from its establishment. The Spanish were not in absolute dominion of their colonies in those times needing protracted wars, negotiation, and power-sharing to keep control well into the establishment of the post-Revolution states across South and Central America. Much is the same of the French and British Empires, their peak of control only lasting about 100 or so years across their vast holdings in the Americas, Africa, and Asia.
500 years of domination is not the history of Europe, let alone the history of the empires that did have massive global impact. If we want to properly define another region pulling off the same, categorising proper achievements (we could work with the spread of religion qualified with how much religious authority is in the Imperial metropole, perhaps trade? flow of wealth? Language spread? Influence contemporaneously?) Empire is an action of continuous mounting struggle that almost always costs more than it did to maintain. It traumatises millions of both oppressors and oppressed for what? Which regions can maintain such an effort?
You could have certainly gotten more regional empires or rather, continental empires. Sprawling land empires alla Russia or Mongolia require a lot of empty land to maintain the fiction of control. Taiga and desert aren't going to contest sovereignty, after all. Maritime empires required initial contact to be largely beneficent in first contact and munificence on the part of those initially contacted.
Asia has been mentioned as a contestant for global dominance, both West and East. However, they would certainly have completely different strategies of expansion, conquest, occupation, and potential settlement (or perhaps decline? Client establishment? vassalage?) As would North African Kingdoms.