Perhaps the OP meant "nigh", which is archaic, and means the same as "near".
Even then, "nigh beneficial owner" and "near beneficial owner" are awkward constructions that would have broken the continuity of my reading comprehension.
But surely one is or is not a "beneficial owner". Being nearly a beneficial owner is the same as not being a beneficial owner at all.
I think "nigh" is meant to modify "owner", not "beneficial". I think the lawyer saying is saying that the KSA figuratively owns Twitter, and that Twitter benefits from that relationship. Golden handcuffs, basically.
That is the most awkward phrasing I've seen in a long time. I'm not even sure it's grammatically correct. I would've expected "beneficial nigh-owner" or something like that.
I found a couple of usages in academic publications, but they don’t give me any more context as to meaning. That leads me to believe that it’s not a legal term.
I can’t find any meaning other than the “sound a horse makes” in any dictionary, either.
ETA: Apparently, the old English “nēah” meant “near”. That seems to be the the root of the work “neighbor”.
Interestingly, it looks like “neigh” (like a horse) and “neighbor” both came into use in English in the 12th Century. Perhaps coincidental.
Has anyone seen this use of neigh before? Is it a legal term? What does it mean?