Ethnicity has nothing to do with genetics. Dictionary definition says "a social group that has a common national or cultural tradition"; Wikipedia has this starting paragraph:

"An ethnic group or ethnicity is a category of people who identify with each other, usually on the basis of a presumed common genealogy or ancestry or on similarities such as common language or dialect, history, society, culture or nation. Ethnicity is often used synonymously with the term nation, particularly in cases of ethnic nationalism, and is separate from but related to the concept of races."

>usually on the basis of a presumed common genealogy

From Wikipedia. You're right that I didn't list every factor.

"Presumed" is the key point. e.g. Ethiopian Jews have no genetic relationship with other Israeli Jewish subgroups, people in Eastern Germany have just as much in common genetically with Poles as with Western Germans, etc. And when these things are brought up, many ethnic nationalists will shrug their shoulders and say "so what".