Earlier quoted context omitted.
Races are extended families. People in a race are genetically and genealogically closer to each other than to people outside of it. This racial clustering of relatedness is empirically testable. Race is not a social construct.
You're using a fairly prescriptive definition of race. Race, as commonly used, is a social construct. Ancestry functions the way you describe, but as the example given above shows, "race" and ancestry are not directly related.
Of course they are.