I think the greater offensive output has less to do with rule changes (although they certainly play a part) than coaches slowly recognizing that passing the football is a better way to score points and win football games. For decades, NFL coaches were biased in favor of running the football—“only three thing can happen when you pass the football, and two of them are bad”, “you have run and stop the run”. Much of this realization can be traced to analytics; passing has always been a superior way to move the football; it’s just taken football people a long time to understand that.
As a result, teams are throwing more, devising better, more difficult to defend passing concepts, and devoting greater resources to developing the passing game. As defenses try to adjust, some smart coaches (like Belichick) will exploit it by going run-heavy against defenses geared to stop the pass, but that won’t change the basic fact: Passing is better.