The author's explanation of what characters Chinese, Japanese, and Korean share is very limited. All three languages use Chinese characters in written language to varying extents, and in some cases the differences begin significantly less than a century ago. Though there are cases where the same Chinese character represented in Japanese writing is different from how it is represented in Traditional Chinese writing (i.e. 国, Japanese version only because I don't have Chinese installed on this PC), which could be different still from how it is represented in Simplified Chinese, there are also many instances where the character is identical across all three languages (i.e. 中). Although I am not privy to the specifics of the CJK unification project, identifying these cases and using the same character for them doesn't sound unreasonable.
Edit- To be clear, Korean primarily uses Hangul, which basically derives jack and shit from the Chinese alphabet, and Japanese uses a mixture of the Chinese alphabet, and two alphabets that sort-of kind-of owe some of their heritage to the Chinese alphabet, but look nothing like it. If they are talking about unifying these alphabets, then they are out of their minds.