My guess would be that he knows the literati Chinese well (especially if he enjoys hanging out with the educated types, and being able to read such texts as he encounters), and is probably conversant with some of the major dialects of the places he's been. (Which means he might be able to fake it with related dialects, especially if the other person is patient.)

For nicknames and the like, you could fake it with modern dialects. I don't know how much information we have on what was being spoken only a few hundred years ago. (But again, that's not really my time period.)