here an explanation
As a linguist, I find that their “connections” are tenuous at best. I would have to read a peer-reviewed paper that goes over their arguments in greater detail to make any final conclusions. However, in the article you linked there are simply superficial similarities in basic syntactic structures and argument ordering. You could find similar comparisons between English and some random unrelated language if you look hard enough. There are nearly 7,000 languages in the world (Eberhard et al. 2020), and there are bound to be superficial connections like this. Ultimately the only reliable way to prove that two languages are related is through the comparative method, which they do not use and could not use in a language contact situation such as this. Therefore, unless archaeology supports the “linguistic evidence” (which is questionable at best based on this article), then I would take this all with a grain of salt.
Sources:
Eberhard, David M., Gary F. Simons, and Charles D. Fennig (eds.). 2020. Ethnologue: Languages of the World. Twenty-third edition. Dallas, Texas: SIL International. Online version: http://www.ethnologue.com.
"Celtic" isn't a straightforward term at all, so things here get pretty complicated pretty quickly. :D
Here are a couple of earlier answers that might interest you!
Did the Celtic peoples "arrive" in Britain, or did Celtic culture just spread to the bronze-age inhabitants of the island? - one user has deleted their account; the other answer is by /u/tbickle76
Were Celtic people the only ones who populated Britain before Anglo saxons? and could you give me some info about Scottish people please? - by /u/depanneur and /u/geisendorf
And this great earlier answer by /u/depanneur talks about the idea of "Celtic" as a culture/people on continental Europe versus Britain/Ireland, including language origins and shifts:
From a linguistic point of view, there are three possible leads as to Pre-Celtic Irish people.
Neolithic Inhabitants of Ireland
A common set of borrowed vocabulary in Proto-Germanic, Proto-Finnic, and Proto-Celtic
A substrate found solely in Irish, which might correspond to the language of the Partraige people of early historic Ireland.
The first, the Neolithic Irish, rests on the fact that most Neolithic inhabitants of Europe were a genetically distinct population deriving from Anatolia. Since the spread of agriculture in Europe was primarily a movement of this specific people group, it stands to reason that they brought their language(s) with them into Europe. What these languages were isn't well understood; a widely discredited theory states that Proto-Indo-European spread with these farming peoples. Linguist Peter Schrijver (you'll be hearing his name a lot here) has proposed that these Neolithic languages were related to Hattic, an ancient indigenous language of Anatolia by analyzing substrate vocabulary across various Indo-European languages. He finds that they both share a unique feature: a suffix (h)a- which alters the semantics of a word very little but triggers vowel reduction inside the stem. He goes on to compare Hattic and the aforementioned substrate to Minoan and Sumerian. The Neolithic Irish people may well have spoken one of these Neolithic languages.
For the second one, there exists a shared set of foreign vocabulary in Celtic, Germanic and Finnic. These words often alternate between a geminate consonant, nasal+stop sequence, and a long vowel+short consonant, a variation inexplicable except via borrowing. Many of these words are transparently Indo-European, however. Schrijver proposes an Indo-European language spoken in the British Isles, Northern Europe and Scandinavia which he calls "The Language of Geminates". He further proposes that, among groups which spoke this language, the Manapioi and Kaukoi tribes of ancient Ireland should be included.
For the third one, there are some inexplicable words only in Irish. Among these is partán "crab". There are a people called the Partraige in early Ireland, nearly always subjects, living in a mountainous area (a common refuge for besieged indigenous populations), whose name is derived from the aforementioned partán. Schrijver proposes that this language gave a substrate to Irish. This language could have survived as late as 500 AD. Schrijver proposes that either Partraige or The Language of Geminates could have affected Irish word order.
[Lost Languages in Northern Europe by Peter Schrijver 2001, Pruners and Trainers of the Celtic family tree by Peter Schrijver 2015, Talking Neolithic: The Case for Hatto-Minoan and its Relationship to Sumerian by Peter Schrijver 2019]
Regarding Insular and Continental Celtic language(s), are there any comparative studies between Gaelige and the Basque language? I’m familiar with Gaelige coming from Ireland, and have often heard that Basque is the oldest language in Europe alongside the Irish language, in part because they share a similar history. Is there any truth to this, and/or have these languages crossed paths in some meaningful way historically?