Civilization might be the wrong word to describe China's historical influence on the surrounding region. Culturally each nation in the region differs from each other, add social stratification, economic policy, human rights approach and other metrics and too many differences occur. Like Greece, China has helped shape a region (or in Greece's case, formulate a cultural and governmental path), but also like Greece, China's influence waned and allowed other nations the chance to form their own paths. The US is no more like Greece than Japan and China are the same. I agree with the jist, but not the semantics.
Historically speaking, tho, the Yayoi people of Japan came from the Chinese mainland. This is the reason why present day Japanese are genetically linked with Han Chinese. We share a substantial mitochondrial haplotype with them.
Genetically speaking, Japanese are very close to Chinese people. In fact, our ancestors came from China....thousands upon thousands of years ago.