Tim, I can't predict the outcome of this development but the analogy with the NFL/AFL or the NBA/ABA has serious flaws. In both cases, the players had no role in the ownership of the sport. It was restricted to a group of mostly rich owners (Green Bay excepted) The leagues were started by another group of wealthy individuals who wanted "in", whether for ego or economic reasons. The players were largely underpaid and the leagues were relatively small so there was an ample supply of players to make for entertaining play. There was no "ethical" issue involved in the new leagues' ownership. The mergers occurred as a means of cost control and to improve public perception of the competition. While the same factors might ultimately militate toward a compromise, the Saudis are not motivated in this case by economics so that they have less incentive to compromise.
Here the Tour was founded by the players and while the Tour has a well established management and outside directors, the Player Directors continue to have a significant say. There is no "ownership". Instead, each tournament has individual sponsors. Indeed, one of the purposes of requiring releases is to obtain representative fields to satisfy sponsors. But if a sponsor is dissatisfied or becomes unpalatable, the Tour can find a replacement without significant harm.
LIV has one sponsor with some significant baggage. The competitive aspect, which was unchanged in the NFL/ABA examples, is altered by the guaranteed money, the 54 hole format, the team concept etc.
I could suggest many other differences. But I find it interesting that I have yet to hear any of the players who have jumped discuss LIV's plans for charity. Clearly there are tax benefits to the Tour but it is undeniable that the current system benefits many charities. Will the Saudis do the same? The web site for LIV is notably silent.
Again, how this shakes out is beyond anyone's predictive powers. But we can do better in our analysis of analogous situations and of the likely impact if the LIV tour succeeds.