score:7
Europeans knew about China, India, and South-East Asia. In fact, at the time, the Indies referred collectively both to what we would call the Indian subcontinent and South-East Asia.
As can be seen in this reimagining of Toscanelli's 1474 map of the Atlantic Ocean, Columbus thought:
These statements were controversial at the time, as the Greeks had shown Earth was much larger. When the inhabitants he met in the Americas did not match prior descriptions of the Japanese, he imagined these inhabitants had originated in the Indies.
Reference: https://en.wikipedia.org/wiki/Christopher_Columbus#/media/File:Atlantic_Ocean,_Toscanelli,_1474.jpg
Upvote:2
The third book of Marco Polo's travels deals with South East Asia in chapters 5 to 11. Chapter 5 deals specifically with the South East Asian mainland. So Europeans actually had first-hand accounts of some of those places, plus a lot of hearsay.
Re. "India": It is not really clear to me whether Marco Polo considers South East Asia part of India or not. With Yule's translation, one could clearly come away with the impression that for Polo, even Cipangu/Japan is part of India:
Now that I have told you about the ships which sail upon the Ocean Sea and among the Isles of India, let us proceed to speak of the various wonders of India; but first and foremost I must tell you about a number of Islands that there are in that part of the Ocean Sea where we now are, I mean the Islands lying to the eastward. So let us begin with an Island which is called Chipangu.