When has the League ever been referred to as "the event"? It's always the "tournament" (or conference, as the dub puts it). There is a winner of the tournament. After that, the tournament itself is over. There's a presentation, but nothing more.
The literal definition of an exhibition match is something that exists outside of a competition. Ergo, the match with Kukui is not part of the League, or the tournament to which most people would usually refer it. Especially when it's the only odd man out of a battle after the handing of the trophy that always concludes the League. Now, if the trophy was handed to Ash after the Kukui battle, you might have a point, but it happens after that moment that in all past series concluded the League.
Which puts it in the implication corner of: 1) the Kukui match is not part of the League or 2) Alola follows nothing regarding the rules of a normal League and thus anything it does shouldn't be considered a formal League, completely destroying its validity. In the interest of being fair, I prefer the former interpretation.
EDIT: For the record, too, in past series, when they would declare the "[Insert Region] League open", it was always to signal the start of the tournament. As in, the League doesn't start until the tournament does, so...kinda reinforces my point.