MF-W, I felt the same way you did at first. But in truth this is an extremely borderline case that the policy can allow to go in either direction. There have been further discussions both here and here. Let me summarize a key point here, and then suggest what I think the real issue is.

Culturally, the comparison to Latin is apt. Literary Chinese was unquestionably the lingua franca of the region, and people everywhere used it. And the writing system of Literary Chinese was definitely used/adapted for other languages like Japanese and Korean. On the other hand, neither of those languages is actually linguistically descended from Literary Chinese. Korean is a linguistic isolate, while Japanese is only related to some languages used in and around Japan and neighboring islands. So Chinese is the clear principal descendant of Literary Chinese; it's not like Latin, where there are several strong descendants.