Taleb is trying to say that the Mycenaeans shared ancestry with people of the Middle East, and didn't share ancestry with "Nordics", or at least shared less ancestry with Nordics than with people from the Middle East.
First, "of course" they shared ancestry with "Nordics", by which he means Northern Europeans. Just look at the graph above: all Northern Europeans have some component of LBK, which is extremely similar to Anatolian Neolithic farmers, and that was the largest component in the Mycenaeans. All Northern Europeans also have some percentage of CHG, which is like Iran Neo with some EHG. That Iran Neo was a minor component in the Mycenaeans. Finally, the Northern Europeans have EHG/WHG, which the Mycenaeans also had through their steppe ancestry.
Now, somebody could do some exercise on modern Turks or Lebanese if Taleb prefers. What they would find is some Anatolian Neo, but much less than in Mycenaeans. They'd find Iran Neo, more than in Mycenaeans. They'd find Levant Neo in the case of the Lebanese, which the Mycenaeans wouldn't have except as an ancestral part of Anatolian Neolithic. They'd find no EHG. That could then be compared to the Mycenaean numbers and the Northern European numbers.
I don't know what it would show; maybe the Mycenaeans would share more genes with the Lebanese, maybe not.
What does it matter?
The Mycenaeans were their own unique blend of genes, with their own culture, drawing from both the Near East and the steppe. It's not for either the Nazis of old or Middle Easterners of today to try to claim them or their accomplishments. Neither is it for people in the Balkans to try to claim because some minor percent of their ancestry might have come from Anatolian Bronze Age that means they're Near Easterners and not "pure" Europeans like other peoples of the Balkans. It's particularly ridiculous for Albanians to claim that because they're a subset of Greeks and as such have that ancestry as well, as do other people in the Balkans like Romanians and people in Italy.
I've been in this "hobby" for more than 12 years and throughout all that time internet t-rolls of the "Nordic" or "Slavic" persuasion, and Middle Easterners have been pulling the ancient Greeks and Romans between them, each trying to claim them and their accomplishments. It's got to stop. The Near East is the beginning of Western Civilization; there's an enormous amount of which to be proud if your aim is to be proud of your ancestors. There's no need to try to claim the accomplishments of ancient Greece and Rome, which were their own cultures, building something new based on what they learned from the east.
For that matter there was no need for the Germans of the 19th century and the first half of the 20th century to try and claim Rome's greatness. In the last few centuries they also contributed a great deal to the world. As others have noted, I don't see them involved in these kinds of cultural appropriation today. It mostly comes from Eastern Europe. Maybe, given their history, it's more understandable, but it has to stop, and they have to stop their fanatic and insane anti-semitism from coloring everything they study. It also has to stop among Near Easterners. It's nice to be admired, but their culture was not yours even if it was influenced by your ancestors.
I get Taleb's point about anti-Semitism and how it is tied to a lot of internet chatter about the modern Greeks and Italians, but the answer isn't to make claims that are based on a faulty understanding of genetics.