The debate on whether being Jewish is a religion or an ethnicity or a nationality is ongoing and complicated -- like everything else Jewish. But for me, the interesting thing about this was how it conforms to the version of history I learned 25 or so years ago in Jewish day school: common ancestry in Israel, large split in population after the First Exile where a substantial population remained in Babylon/Persia (modern Iraq and Iran). Then gradual spread westward through the Roman Empire with major population centers in Italy expanding into central and southern Europe, then east again into Eastern Europe, while communities in the Islamic world (notably Cairo, Israel, Syria, and Persia) moved west with the Islamic conquest through Northern Africa and to Spain. I also learned there was considerable cross-over between the communities, which the genetic testing appears to confirm and is a surprise to popular wisdom.
I also note that the two groups identified as not sharing the genetic link -- the Ethiopian Jews and the Indian Bene Menashe -- have somewhat different self-histories that fit the conversion model.
This shouldn't cross into politics, but of course it does. Nation states are not (and should not be) built on genetics, but a substantial effort has been made in recent years to develop a history that would weaken the narrative of Jews a people descended from common ancestors in Israel who pined for an ancestral homeland for 2000 years. Hence, a lot of recent scholarship has tried to establish the the real origin of Ashkenazic Jews in particular (the original Zionists/settlers) is actually Eastern European or Asian (depending on where you place the Kahzars).
Which brings me to one of my usual pet peeves, making more of genetic testing and science where it is. I find this interesting, and it is always pleasant to have one's view of the universe and oneself confirmed. But it does not actually impact the more pressing question of how a group of people showing up after 2000 years, applying a 19th Century doctrine of self-determination and sovereignty settle that claim in conflict with the people already living there, or who have moved in recently. (Palestinian history being itself complex, and there is an equally large body of literature devoted to showing that the majority of modern day "Palestinians" derive from Arabs living in neighboring countries who moved into Palestine during the period of 1900-39 in response to improved economic conditions brought on by the Jewish Aliyah and British Mandate. The fact is that in the 19th Century, the place was a desolate dump with an extremely low population density. This increased dramatically during the relevant period of 1900-39. Some of that was natural increase, some immigration. But how much, and in what proportions, and does it matter?)