I know this is a speculative question, but I am fascinated by ripple effects through history. Is there a chance that indirectly, the Mongolian's conquering of competing civilizations, paved the way for Europe's rise and (skipping many, many steps), ultimately to the great world wars?
What power vacuum? There were plenty of other civilizations that hadn't been destroyed and many empires would rise post Genghis. It's way too much of a stretch to make that claim and even to make that argument would require a lot of evidence to support that frankly would be quite prone to debate. If you're looking for an explanation to the modern standard quota and how Europe and the West rose to dominance in global politics and economics you should read "Origins of the Modern World" by Robert Marks. Not infallible or without its criticisms, but it is a fairly easy read and covers much of the time between the Mongols to the 19th century and many different regions and topics such as "The Golden Age of Islam", mercantilism, population growth, industrial revolution, colonialism, opium wars, the silver mines of potosi... And on and on.
I'm curious about whether this could have also influenced the structure of SE Asia, as well.