If this is alternate history, I can see some PODs that can get something like this.
The most obvious is that the Arabs beat the Chinese to the Eastern continents. In IOTL, it was very close. If the Andulasian Caliphate held together, they could have taken over the native kingdoms instead of China. And with the mineral wealth discovered there, they could have taken other territories, even those islands in the southeast that were also colonized under the Ming. An Arab state based in one of the Eastern continents could also have grown very powerful.
The less obvious but even more intriguing possibility is the Franks not getting wiped out in the great plague. At the time of the plague, they had seized much of Andulasia already and recent archeological discoveries have found that their ships had already reached the Eastern continents, though further north than the territories on this map. The Franks were more advanced than their popular image has it. A Frankish kingdom based in Andulasia could have gotten across the Further Sea as well.
And yes, if the Ming don't restart the great voyages again as in IOTL, and the Arabs or Franks don't get there, maybe you could have had an empire based on the Eastern Continents. I don't think something like shown on the map is likely to come from this, because there simply wasn't much if any contact between the natives on the northern and southern continents before the Chinese arrived.
Andulasia is actually the logical starting points for expeditions moving west across the Further Sea. As for the sliver that isn't covered, that is obviously some sort of tributary state, its rulers probably related by marriage to the rulers of the empire.