Jack Wetherford's recent book on the impact of the Mongols on world civilization and technology would be a very useful tool for such a timeline and save a ton of research. His other books for that matter would be useful as well as he studies a lot of the interface and economic development impacts of nomadic tribes and settled civilizations. It's been several years since I read that book (highly recommended for anyone) but:
China's empires, Persia, Northern India, Afghanistan, Georgia, Russia, Korea wouldn't fall as far or hard as they did with Mongol conquest and slaughter of whole cities, only plagues would have similar impacts and still not as devastating.
So world history would shape up far differently as much of the focus has been on what countries NOT devastated by Mongols accomplished over the next 400-800 years. This is right around the period that these advanced societies stopped and mostly fell behind (Wetherford disagrees and sees a lot of technology transfer and free trade zone in the Mongol empire as a bounty for the whole Eurasian continent.
The ancient Silk Road connecting China with Europe would continue to function fully and the Central Asian empires would continue to be rich and advanced because of that constant infusion of new ideas from trade across the continent. So great news for Samarkand, Kazakhistan, etc. and we'd not have heard of Marco Polo, Roger Bacon, Johannes Gutenberg, or others who later brought Asian knowledge to European attention and were credited with inventing it by local scholars.
Europe would remain the distant backwater it had been or the Renaissance would come earlier with the Asian and Middle Eastern knowledge infusions continuing and accelerating with trade.
"Trivially" I guess for geopolitical history, many millions of people would live rather than be slaughtered or enslaved, live within their extended families/clans/cities and with the accumulated knowledge of their place and resources...disrupting that is very expensive to progress (and the dead people, looted/burned cities and farms, abandoned millenia of infrastructure and fields/orchards/mines, etc.). Statistically that tells us tens of thousands of geniuses, great artists, master craftspeople, master traders, etc. were lost to Mongol arrows, lances, and sieges making the progress lost a good question as some of those regions never really recovered. Certainly many who would have made major impacts on the world were lost with Europe and the Middle East having a relative vacuum with so much of the competition dead and crushed so long.
Weatherford points out the last of Ghengis Khan's descendants/ruling dynasties lasted into the 1920's (Persia?) and it considerably eclipsed Rome's empire in size, population, diversity, duration, cities, and resources. In reality it's as big of a POD as the Etruscans stamping out their troublesome neighbors to the South on the Italian peninsula at a stage where only Etruscan histories might mention the several small battles it took one summer.