Did you not see the excerpt from Wikipedia that I posted (which cites expert studies and assessments)? If not, here it is again. I'll boldface the parts that speak to this group being a distinct ethnic group:
I went there (you should have included a link, not just copied and pasted an excerpt, but oh well) and clicked on footnote 14, the only citation behind that second paragraph. And guess what. Its focus is on showing a south european origin for Ashkenazi Jews (the same origin as Sephardi Jews, and south european gentiles). It does use the term "ethnic group" (though only twice and off handedly) and seems to use "self defined" ethnic group. IOW when they tried to compare genetic similarity of Ashkenazic Jews with North Europeans and South Europeans, they identifed Ashkenazic Jews by asking "are you Ashkenazic?" And they call THAT membership in an ethnic group.
Nowhere do they explicitly define the term "ethnic group" or defend it. So yes, population geneticists do offhandedly sometimes use the term, which is a problem. As for the Wiki article, it places much more focus on the term than the cited article does. While Wikipedia can be a good source, sometimes editors do go beyond what their citations would justify.
By the way, 15% of the "ashkenazi group did NOT show south european origin. So if South European origin is what you consider the Ashkenazi genetic marker (as opposed to other eastern europeans) then 15% of self identified ashkenazi Jews (IE ethnic ashkenazis per the study) were NOT ashkenazi. Hmmm.
Again, the confusion is taking a population (more or less arbitrarily defined) that has a charecteristic that by frequency, can distinguish it from another population and calling it "an ethnic group".
All the lawyers in my synagogue, as a population, likely have a higher chance of being tay sachs carriers than the general population of greater Washington. That does not mean that "the lawyers at my synagogue" (who include Jews by choice, mizrahim, etc) are "an ethnic group".
You are missing what is problematic. Its not the empirical fact of this or that gene frequency among any particular population. Its the conceptual problem of stating that some particular population gene frequency makes it "an ethnic group".
Since you like Wiki maybe this will help
https://en.wikipedia.org/wiki/Ethnic_group#Ethnicity_and_race
also this
https://en.wikipedia.org/wiki/Race_and_genetics#Utility
It has been argued that knowledge of a person's race is limited in value, since people of the same race vary from one another.[7] David J. Witherspoon and colleagues have argued that when individuals are assigned to population groups, two randomly chosen individuals from different populations can resemble each other more than a randomly chosen member of their own group. They found that many thousands of genetic markers had to be used for the answer to "How often is a pair of individuals from one population genetically more dissimilar than two individuals chosen from two different populations?" to be "never". This assumed three population groups, separated by large geographic distances (European, African and East Asian). The global human population is more complex, and studying a large number of groups would require an increased number of markers for the same answer. They conclude that "caution should be used when using geographic or genetic ancestry to make inferences about individual phenotypes",[68] and "The fact that, given enough genetic data, individuals can be correctly assigned to their populations of origin is compatible with the observation that most human genetic variation is found within populations, not between them. It is also compatible with our finding that, even when the most distinct populations are considered and hundreds of loci are used, individuals are frequently more similar to members of other populations than to members of their own population".[69]
and
Usage in scientific journals
Some scientific journals have addressed previous methodological errors by requiring more rigorous scrutiny of population variables. Since 2000, Nature Genetics requires its authors to “explain why they make use of particular ethnic groups or populations, and how classification was achieved.” Editors of Nature Genetics say that “[they] hope that this will raise awareness and inspire more rigorous designs of genetic and epidemiological studies.”[81]