It "is" interesting, and it was an interesting paper.
Do you remember all that blather from "Kurganists" about how the Indo-Europeans were responsible for the achievements of the Sumerians?
Looks like there was no EHG like gene flow until the Iron Age, and even then it's paltry. The madness which people used to be able to spout is amazing.
You can also see how Natufian shrunk in the oldest or most unchanged Levant populations, people like the Lebanese, especially the Christian Lebanese, and the Druze, and how the migrations with the Muslim invasions of tribes from the Saudi peninsula increased it in people like the Palestinians and Jordanians.
The best example, however, is the Assyrians and the Muslim Iraqis. Look at the difference in Natufian. Same for the Iraqi Kurds. Holding on to their religion reduced gene flow.
I can't wait until we have lots of first millennium B.C.E. from the area the Romans called "Greater Syria".
I'm surprised there's so little SSA, but that's probably down to the fact they're using a West African source instead of an East African source, when most of the 'mostly' female slaves came from East Africa.