Yes, this one continues to push back against the modern "there wasn't a big war or anything, people were just inspired by their neighbour's wonderful pottery" theory. It reports massive immigration into Ireland in the neolithic, followed by near-total replacement of the population in the bronze age (to the extent that they think the neolithic remnant elements in the BA samples are more likely to be german, from before the migration to ireland, than native irish).
In terms of the Bronze Age, the population appears to be basically modern Irish (complete with our famous haemochromatosis); the problem is, they were in Ireland by 2000BC. While I can imagine proto-celtic deriving from PIE by then, it seems implausible that the modern celtic languages would have separated so little in 4000 years, so presumably this Irish population must have been pre-Celtic. And it's unlikely that Ireland would have been the birthplace of proto-proto-Celtic, so we're talking a non-Celtic, pre-Celtic population. However, it was clearly steppe-derived.
[To put that another way: if these people were Celtic, that means we need to assume that either a) Irish, Welsh, Gaulish, Celtiberian etc were in place four thousand years ago, and that by AD 0 there had been at least two millennia of differentiation between these languages; or b) other Celtic languages are a result of a mass migration out of Ireland. The first seems improbable, and the second seems extremely implausible.]
This raises two possibilities: a non-IE steppe language that invaded Europe alongside, or prior to, PIE; or a non-Celtic branche of PIE that swept across Europe before the Celts got there.
Bringing in archaeology, we know that these BA Irishmen were Bell Beaker People, or had at least adopted their culture (and if we're saying that both a cultural and a genetic change had just happened, it seems easiest to assume they happened in one go, i.e. the culture came with the migrants). So the Beakerfolk (at least, by the time they reached Ireland) were either an early branch of IE, or something else. The obvious candidate for 'something else' is Basque, in which case Vasconic would have been another steppe-horse language out of the east, that just happened to get drowned out by its neighbouring ally, PIE. This would suggest a PIE-Vasconic family, though wouldn't require it (two different pastoralist groups could live side-by-side on the steppe with totally different languages - the Hungarians, for instance, presumably lived as steppe pastoralists alongside Turks, and various Turkic groups have lived closely alongside Mongols. Though we might perhaps expect to see more similarity between the languages, if this is the case - even if not genetic, at least areal similarities.
Ockham's Razor suggests the Beakerfolk in Ireland were probably IE-speakers, of an unknown early branch, perhaps or perhaps not a cousin of Italo-Celtic (perhaps Lusitanian is a parallel here - similar things have been suggested for it). This is more plausible than positing a second, unattested steppe family with the same genes as the PIE - especially if we take things like R1b as evidence for the Basques having a big Beakerfolk influx, as that would mean the Basques would have to accept genes from, but not language from, two invading groups in a row.
[Alternatively, re Basque: we could still see the Beakerfolk as Vasconic in origin in Iberia, but with the culture (and perhaps language!) adopted by incoming Yamna in the north - but this seems overly complex as a default assumption, given the total lack of evidence, and the probable connection of the Basque R1b with the steppe]
It's worth pointing out that the Basque and the modern celts, other than their R1b, don't look particularly closely related. The Celts are much more steppey. So I think the parsimonious model is still that PIE Beakerfolk became the modern Irish, the celts invaded and brought their language at some point but didn't massively change the genetics (the beakerfolk being their cousins already), and meanwhile the Beakerfolk and/or celts were bringing some R1b bloodlines into the Basque. Since R1b is paternal, that's not hard to imagine - some horselords conquer the place and have lots of sons, but the culture remains largely unchanged.
Turning to the Neolithic, we see that the Farmers reached Ireland. Specifically, the strongest connexions are to the Cardians, via Spain, rather than with the LBK from Germany. The paper links the Cardians with passage tomb culture spreading from Spain to Scandinavia, and notes the similarity of the Irish sample with one sample of Funnelbeaker in Scandinavia - apparently Funnelbeakers are mostly considered LBK-related, but the sample in question was from a megalithic tomb. Of course this could just be general mixing, but it raises the question whether perhaps the Cardian-derived passage grave culture might in some places have been a ruling class over LBKs?
This all looks like bad news for Basque. We knew that the Irish looked like everyone else, but now we know that this was true even in the neolithic. If the Cardians reached Ireland, and via the coast as well, it makes the chances of a mesolithic hold-out on the atlantic coast seem much smaller, I think. Of course, genes don't determine language - but big genetic changes do at least make language change more likely. On balance, I think the most likely option now is that the Basque linguistically represent a cardial-ware/passage-grave remnant, rather than a palaeo/mesolithic one.
The Irish mesolithic genes in the neolithic sample, incidentally, look pure western, without scandinavian or eastern HG contributions, which makes sense - as the ice retreated, the British Isles would probably have been settled in one movement. Apparently these WHG genes look closer to genes from Luxembourg (which are also related to those in Germany, Denmark, switzerland, etc) rather than those from spain or france.
Just for fun: as you probably know, Irish legend reports six invasions of Ireland. First Cessair and her people came, but they had only three men so they died out quickly and there was no-one left on the island. Then Partholon came, defeated the Fomorians, and died in a famine so there was noone left on the island. Then Nemed came and defeated the Fomorians, but then his people were enslaved by the Fomorians and destroyed and the survivors scattered. The remainder went to Britain, Greece, and the North. The Greek lot came back as the Fir Bolg. Then the Tuatha Dé Danann came back out of the North, exiled the Fir Bolg to Connaught, and defeated the Fomorians. Then the Milesians came out of Spain, defeated the Tuatha Dé and exiled them to the underworld.
If we now have to talk about Mesolithic, Neolithic, Beakerfolk and Celtic waves, we're coming close to the six! [The older accounts only have three settlings - those of Partholon, the Tuatha Dé, and the Gaels]
In fact, we can probably add an additional neolithic wave - features like chambered cairns and grooved ware probably came from northern scotland. The tombs were later associated with the Tuatha Dé - in their post-exile, underworld incarnation they are known as the People of the Mounds. And it's hard not to want to associate the Tuatha Dé, who came out of the northern islands of the earth and were cousins of the Fir Bolg, with the grooved ware people who came from the orkneys via the hebrides and were cousins of the native neolithic population...
There seems to have been some awe around the tombs all along: the Beakerfolk were a less dense population than the Neolithics (whose population seems to have crashed), and seem to have squatted around the edges of old Neolithic settlements and tombs. And we can add a sixth wave if we postulate that the Gaels did indeed, as all the legends say, arrive by sea from Iberia, presumably replacing a Brythonic population.
[If you're really keen on myth, you can link the Fir Bolg - a seaborne population from the periphery of Greece - with the Sea Peoples...]
But the river tripped on her by and by, lapping
as though her heart was brook: Why, why, why! Weh, O weh
I'se so silly to be flowing but I no canna stay!