Besides the arguably ad hoc correspondences between PIE roots made to look similar to the Sumerian, with several irregularities (e.g. in some words final -eh2 disappears, in some others it becomes -ah), which were pointed out in the article I linked above (some of the supposed cognates sound really forced to fit into the Sumerian word), for me it is really difficult to reconcile this hypothesis with the more accepted chronology and geographic/archaeological traces of PIE. I mean: Proto-Anatolian split being dated to ~4000 BC, Early totally undivided PIE is dated to immediately before that date; Sumerians are thought to have been present in Sumer at least in the later mid of the 4th millennium BC, so that leaves around ~500 years between PIE and Euphratic before it was replaced by Sumerian (and that must've been pretty early, because as far as I can see Whittaker's Euphratic is basically undifferentiated PIE, with few changes).
Therefore, we must find an explanation (in genetics and archaeology) that fits an early presence of the very same or virtually identical PIE in both the Pontic-Caspian steppe (definitely associated with the expansion of most of IE branches, Anatolian excepted perhaps) and more than 1500 km to its south in South Mesopotamia/Sumer. Such a linguistic closeness should then indicate a very recent migration to or from the Pontic-Caspian area from or to South Mesopotamia. It must've been a migration bringing a different culture and probably ethnic/genetic makeup roughly between 4500-4000 BC, because after that Euphratean would've been the language of newcomers, not the supposed established language of a proto-urban people who supposedly invented writing (not the Sumerians, as per Whittaker's hypothesis), or PIE in the steppes being spoken by pastoral primitive tribes would've been the very recent arrival coming from a proto-urban farming culture in a totally different environment than the one reflected by reconstructed PIE. For many reasons I just do not see many (archaeological, linguistic, genetic) evidences to back this idea up.
The proportion of R1b-Z2103 is very intriguing, but considering it is found in non-negligible percentages among some Iranic populations its frequency could've exploded more or less recently regionally. I very much doubt a Mesopotamian population by ~4000 BC would not have brought much Levant_Neolithic and Iranian_Neolithic to the Pontic-Caspian steppe, not to mention the apparent organic cultural development without strong ruptures in the western steppe during the Chalcolithic (AFAIK).
If Euphratic is true, then we definitely need to find a chronologically very close (in comparison with the Uruk period when Sumerian was demonstrably spoken) connection between the Pontic-Caspian area and Mesopotamia. I personally would find it a bit easier to believe in a Sumerian-PIE connection not with a substrate language in Sumer itself, but with Sumerian being brought to Sumer from its original homeland much closer and maybe in direct contact with Early PIE or maybe even the parent language of PIE (somewhere in the Caucasus? Or in the Black Sea coast? Who knows).
Well in terms of archaeology there's a decent amount backing it up - of course, I've mentioned the swastikas and metallurgy spreading from the Balkans originally, but what about the overall pretty great similarities between Vinca and Ubaid symbols, figurines and metallurgy? The early 20th century archaeologists saw Vinca as a development of Mesopotamian cultures like that of Ubaid, but now we know if anything it was the other way round - metallurgy is oldest in Vinca, as are the symbols (which bear some similarities, but the extent of this is debatable) and the figurines (those lizardmen people think are aliens).
Also, why could it not potentially be the case that one branch travelled down Mesopotamia, and another continued in the highland region to the North (eventually moving up into the Steppe). That, though, seems like an added complication and so goes against Occam's razor I suppose. But, there is a neater solution - what about
Leyla-Tepe - these guys are theorised to have been Ubaid-period migrants, who brought with them the first metallurgy to the Caucasus, and are theorised to have been founders of the Maykop culture. The fact that Maykop seems to be Y DNA G, J and L could be explained by burial differences or differences in location (the pastoralists might have been in a different region than sampled, as is the case with the Caucasus today lots of different groups can live in a relatively small area isolated by terrain). From looking at where the samples were taken, it appears the Y DNA G, J and L were not found in the Eastern Caucasus - whereas perhaps Z2103 migrated to the Steppe through th easier Azerbaijani-Dagestani route (near to where that Chalcolithic Z2103 was found). Maykop Steppe is just completely mind-boggling to me - how Siberian HG ancestry is there I have no idea. Whatever the case, I'm dead-set on Z2103 from West Asia, which leads the Z2103 of Yamnaya to be Southern in origin. Also, there's the presence of red hair and blue eyes carried by someone with Y DNA L in the Areni-1 cave, that surely is ultimately of R1b origin (so indicating close contact between the two). Caucasian red hair is still preserved in the North, among the Chechens, who actually have an awful lot of it.
As for Sumerian perhaps being the contact source with PIE instead of the substrate theory - firstly, there is that point about "Ur" meaning village in proto-Dravidian which I see as unlikely to be coincidental, but also the fact that the Sumerian migrants are theorised to have invaded from the Arabian littoral (likely the Southern Zagros), which is where the later Elamites were based - and probably not by coincidence, there is the hypothetical Elamo-Dravidian language family (linking Elamite to the Dravidian languages). I think the civilising movement of Iranian farmers eastwards into India was of Dravidian stock, and that the Indus Valley civilisation was Dravidian, only for Dravidian speakers to have been pushed SE by the later arrival of the Indo-Aryans (so, I don't think Dravidian has anything originally to do with what people now consider as Dravidian (Veddoid people like Tamils), but rather Iranian farmers).