Let's see other parts of Reich's lecture
""Our comprehensive sampling shows that Anatolia received hardly any genetic input from Europe or the Eurasian steppe from the Chalcolithic to the Iron Age; this contrasts with Southeastern Europe and Armenia that were impacted by major gene flow from Yamnaya steppe pastoralists.""
""The impermeability of Anatolia to exogenous migration contrasts with our finding that the Yamnaya had two distinct gene flows, both from West Asia, suggesting that the Indo-Anatolian language family originated in the eastern wing of the Southern Arc and that the steppe served only as a secondary staging area of Indo-European language dispersal. ""
This means that they didn't found any evidence of migration from Steppe to Anatolia via the Balkans. Between the Chalcolithic and Iron Age. This is important because David Anthony and some others proposed a theory about Balkanian migration of proto-Anatolians. This would be the second paper addressing this issue. And it seems his conclusion will repeat the one made in Mathieson et al.
We can safely say that IE Anatolian language were introduced to Anatolia from East. There is simply no alternative to this They label that region with a strange term "Eastern Southern Arc". Whatever You call it would be historic Armenia or South Caucasus. And we can say that IE speach was spoken in Armenia the last 6000 years, from which the 4400 years are the formation and spread of Armenian. Not bad at all even if the IE homeland issue remains unsolved in the near future