A Chinese Jew, and there are Chinese Jews, are culturally Chinese. They have no ancestral ties to a place on another continent.
Oh, please. Let's talk about Chinese Jews. Chinese Jews are culturally Chinese because they LOST their Jewish culture (mostly through intermarriage and just time in a very small community). Had they RETAINED their Jewish culture -- guess what?! They'd still be Jews. (They are not actually considered Jews by the Jewish community because they follow patrilineal rather than matrilineal descent).
How did Jews come to be in China? About a thousand of them moved there at a specific time in history, probably from Persia. They didn't "convert" to Judaism -- they were a community of Jews living in China. They retained their Jewish culture and Jewish customs for hundreds of years. It has only been recently that their Jewish culture has been lost.
Irish people move to Canada, and they still have Irish ancestry. Palestinian people move to Chile and they still have Palestinian ancestry. Jewish people move to China and they have Jewish ancestry. The measurement, in the absence of modern technology, is the retention of a culture that moves with people from place to place.
See how easy this is?
"Palestinian people move to Chile and they still have Palestinian ancestry. "
I find it hard to include the new nationality of Palestinians with all others.
Palestinians, Lebanese, etc, if they came from Arabia, they have Arab ancestry from the Peninsula.
Portuguese moved to Brazil, they still have Portuguese ancestry.
The French moved to Canada, they still have French ancestry.
The Spaniards moved to any part of South, Central or North America, they still have Spanish ancestry.
Etc.
The Jews are a long established religion, people, nation, culture and language. They have moved anywhere in the world, from their original ancestral land, for the past 3000 years and have retained their Jewish religion, culture, etc, therefore they are still Jews.
If they assimilate and leave the Jewish religion, they are not considered to be Jews anymore until they choose to return to the religion, as many have done.