Not exactly. What I mean to say is this: We know there are certain phenotypes that predominantly appear in certain populations, in broad strokes. But while we do have lists of correlates, we
don't have good definitions for what an "ethnicity" is biologically, and there is very good reason to believe no satisfactory definition exists.
To use OP's example, we know that the gene mentioned is frequently found in the Inuit population. But if an Inuk does not have that gene, it does not somehow make them less Inuit. We can't quantify percentage Inuitness, and doing so is logically unsound. This is because the term "Inuit" doesn't mean its biological correlates. It simply has biological correlates.
To use an example of a personal friend, slightly anonymized: My friend is an Ashkenazi Jew. There is absolutely no uncertainty about this; Jewishness is matrilineal, and their mother was an Ashkenazi Jew, and her mother before her, going back over eight documented generations of family history. But alas - their grandfather was infertile, a fact that was posthumously revealed. Their maternal grandmother had a sperm donor. The sperm donor was not an Ashkenazi Jew. Consequently, can said friend be said to be "only 75% Jewish," having missed the "necessary" genetic correlates? Of course not. By simple matrilineage they are fully an Ashkenazi Jew.
Why are these terms used in medicine, then? Because, put simply, it's the best we can do. Genetic profiling is a useful tool under some limited circumstances, and asking medical subjects their ethnicity is often useful in determining medical correlates. But there is nothing in the gene that says "I am Inuk, I am Ashkenazi," because these ideas are social first, not genetic first.