East Asia is bound together by a written language rather than by a spoken one. Chinese characters were adopted for administrative and literary use in Korea, Japan and Vietnam, and what travelled on that script is most of what the atlas holds under this heading.
Buddhism is the clearest case. It reached China from Central Asia and India in the first centuries CE and was translated into Chinese over several hundred years by teams working from Sanskrit and Central Asian languages, a project on a scale with few parallels in the history of translation. It then reached Korea and Japan in the Chinese versions rather than from India directly, which is why Japanese and Korean Buddhists have historically chanted texts in a Sino-Japanese or Sino-Korean reading of Chinese, and why the schools of the region, Tiantai and Tendai, Chan and Son and Zen, Pure Land in its several forms, are a shared inheritance with local developments.
Confucian learning travelled the same way, supplying a vocabulary for ritual, family obligation and government that operated in all four societies regardless of what else people believed. State examinations based on the classics were adopted in Korea and Vietnam.
Daoism travelled less far as an institution but its cosmology, its ideas about the body, and its calendrical and divinatory practices spread widely. The atlas keeps China, Japan and Korea as separate regions and uses this entry for what is genuinely shared.