The first item on the list is "magic," an obvious point on the list given it is a key component in every iteration of the franchise. The second is "summoning," which has been a staple of the series since Final Fantasy III. The third on the list of needed components is "gorgeous beauty." This one is interesting as, given the sprite-based nature of the first six Final Fantasies, "gorgeous beauty" didn't really enter the equation until the PS1 era. Still, no doubt modern Final Fantasies are very much into being visually stunning in both design and graphics.
The fourth thing needed in a Final Fantasy is a little ambiguous: "refinement." They didn't specify refinement of what exactly, but each game in the series has at least tried to refine the parts of gameplay that didn't work in the previous iteration. The same can be said of graphical refinement as there can be no doubt that each Final Fantasy has looked better than the previous incarnation (with the possible exception of the MMOs).
Lastly, they stated that Final Fantasies need "change and challenge." The "change" part is obvious, with each numbered Final Fantasy taking place in a new world with a new cast. The battle system also changes from game to game as well. As for "challenge," that is a bit more ambiguous, but it could mean that each world has a challenge that must be overcome. It could also speak to finding the balance in gameplay between tedious grinding and welcome challenge.
So there you have it: what Square Enix thinks are the basic components to a Final Fantasy. For the most part I agree with this list, though I think things like "a world threatening conflict" and "an unlikely group of heroes" are also key components to the Final Fantasy formula... not to mention Moogles. I don't know about you, but I get really angry if my Final Fantasies are Moogle-less.