The correspondence seems remarkable; the only major discrepancy is for Iranic (Indo-European) Ossetes who group with NW Caucasians genetically, which makes sense as the Ossetes are probably to a large extent NW Caucasians that underwent a language shift at the influence of the Alans.
I won’t comment on whether such a link exists, but a relationship between Hurro-Urartian and Northeast Caucasian coupled with the known proximity of Indo-Aryans with Hurrians would immediately supply an explanation for the “Dagestan” component: it might be the legacy of an absorption of Hurrian elements by the ancestors of the Indo-Aryans while the latter were still in the Near East.
By the 2nd millennium BC, the Indo-Aryan element seems to have been well on its way to disappearance in the region, and we find no trace of it after the demise of the Mitanni. A millennium later came the disappearance of Urartian, replaced by various types of Indo-European (such as Armenian and Iranian), and Semitic. We are fortunate that the Indo-Aryans of Syro-Anatolia left traces of their existence before their demise.