In terms of continuity, Constantine's connection to the Arrowverse is peripheral, yes. But I think what DigificWriter means is simply that Constantine has been retroactively established as taking place on Earth-1, as opposed to Supergirl (Earth-38), the 1990 Flash (Earth-90), and all the other old shows and films whose cast members are appearing in Crisis on Infinite Earths.
https://arrow.fandom.com/wiki/Earth-1
It is indeed the intent of the Arrowverse's creators that the John Constantine appearing in Arrow and Legends of Tomorrow is the same version of John Constantine who appeared in the NBC series. That's why he wears the same coat, and why they got the same actress who played Astra Logue in Constantine to dub her faked voice in a Legends episode, and cast her adult version as an African-American like in the show. They're limited in what they can directly reference due to the different networks and creators and all, but it's still meant to be the same John.
What I mean is that, in terms of the Arrowverse as a franchise, NBC's Constantine is as much of an official installment as The Flash '90, Arrow, The Flash '14, Vixen, Supergirl, Legends of Tomorrow, Freedom Fighters: The Ray, and Batwoman.
It is explicitly treated as such by the Arrowverse's producers and writers and its events have as much impact on the overall narrative continuity of the franchise as those other series.