The Mongols don't unify.
China is not devastated and instead has a 13th century technological/economic boom that leads to some industrialization
14th century Japan catches on the industrialization and begins conquering south asian islands to control trade and resources
An Ottoman-equivalent muslim gunpowder empire conquers the middle east and Constantinople, blocking spice trade routes
Japanese merchants try to circumnavigate Africa to get to their destination markets, end up discovering America
With Europe lagging behind and Asia far ahead, the colonization of the Americas goes differently, with separate Japanese clans staking out private charters
By the 18th Century, Japanese imperialist states have global presence, compete against each other, but are loosely associated under the spiritual authority of the "Emperor".
By the 19th Century, the Ottomans have been conquered, and Constantinople is a Japanese city. The Aegean japanese territory becomes interested in local hellene culture, likening the Romans to a European equivalent to China and the Caesars as worthy emperors. A daimyo converts to christianity and takes a greek name to rule a revived Byzantium.
So we have a hellenized Japanese state... in Europe.