I don't think there's any reference to other parts of the world in the novels or the tv series. Rather like trying to guess what happened to China or Russia in "The Handmaid's Tale", we have to resort to speculation.
It seems possible that in the absence of a European colonisation, Africans could well move beyond their continent and establish contact with India and China. The Chinese might have wondered what happened to the Europeans with whom they had traded briefly before the Black Death.
The Chinese treasure fleets would doubtless have met the African Empires as they did in OTL and recognised another Imperial power. Assuming Zheng He's voyages ended with him, however, how and in what way does America get "discovered"?
One possibility is Scandinavian refugees fleeing African incursions might have discovered or re-discovered Vinland in the 1400s (aided by those who had survived on iceland).
Another is Russian settlers pushing east cross the Bering Strait (as they did in OTL) and move down through Canada into North America which in time becomes part of the fourth great world empire.
We also don't know if the Africans are able to move into the Middle East, perhaps taking over the mantle of leadership of Islam.
So, by 1750, you have a African, Indian, Chinese and Russian Empires dominating the globe with only Japan, South America and parts of what we would call the eastern seaboard beyond the reach of these powers. We can speculate on conflicts in the Middle East between African and Indian Empires and between the Chinese, Russians and Indians in Asia.