Here's the basic premise. The Mongols were far more powerful then in our timeline. They were able to take over huge tracts of Asia, but more critically, all of Europe. This pushed European technology back centuries (much as eastern Europe had happen) but allowed a transfer of wealth and knowledge from Europe to Asia. By the time the 1600's come around, it is not Europe who is colonizing the world, but Asia. Asian empires are starting to expand and colonize.
Notable changes as a result of the Mongol invasions
Islam never spreads to Asia (Indonesia in particular) due to Mongol control over the middle east.
India is able to unite into a single empire due to experience as a single nation under the Mongols
The main players on the international stage are therefore
India
China
Korea
Japan
and others. This is all still an ongoing project in my mind. The Thai seem likely to have had a strong empire in place in such a timeline. What happens to Indonesia and the Philippines is more up in the air.
Anyway, I'm curious what others think about this. Who would have been the major players? What would have got colonized? How would things have been different from a world where Europe does this?