That's a fair objection, but given the context I assume he was not actually having anything other than Chinese in mind. Otherwise one might as well bring up Vietnamese, which has a similar history and lexical makeup as JP/KR and is spoken about as far east, but is now written phonetically in Latin-based script with hardly any readers of the old Chinese-based writing system remaining.
Yes, Vietnamese is another great objection, as it's similar to Korean that way. Given that China, Korea, Japan, and Vietnam are the 4 major "eastern" countries then, and only 1 of those might be true for his claim, then why did he say "eastern" instead of just "Chinese"? That's like claiming the American continents (North and South) use English because it's used in the United States. People in Quebec and almost every place south of Mexico will be quite offended, rightfully so.