You're correct on all fronts, but I guess what I would point out is that those design elements were a staple of the FF franchise long before 7. It was another turn based strategy role playing game in a series of turn based strategy role playing games. With OOT you had a real time action adventure franchise with a game using design elements you'd expect from....well, from a turn based strategy role playing game xD
That's where I have issues with OOT in hindsight. It stumbled in executing on its own self-image, whereas FF7 did a better of job of understanding itself
It's literally a multiplayer competitive shooter. That's the game.