It's easy to spread culture when you have a lot of people. But those people all need to be fed. China has one of the most fertile farming regions in the world. Many of the rivers from the Himalayan mountains deliver nutrients east through China, providing great farmlands. It's why China currently has the world's largest population. On the other side of the Himalayas, India enjoys the same benefits which is why it has the second largest population.

The other East Asian nations simply could not produce as much food. Korea is on a mountainous peninsula in the colder north. Japan is an island nation. Southeast Asia is a tropical jungle.

Korea and Southeast Asia "embraced" Chinese culture when threatened with China's large military. Japan took elements of Chinese culture through exchange and trade but it didn't stop China from trying to invade.