“Gaiden”(side story or spin-off) made the game feel too distant, and we wanted to set the right tone for DISSIDIA FINAL FANTASY; it isn’t a numbered title, but has just as much spirit as a main story."
Here, they basically says that they didn't wanted Dissidia Final Fantasy to be an spin-off. It isn't a numbered title either, they wanted the game to be felt like a main story, meaning unique. I don't see anything that suggest they are talking about a canonical reference between Dissidia and the main numbered Final Fantasy series. At least under my standpoint. Maybe you see it as they are meaning that Dissidia is canon.
"As a rule we were extremely careful to treat DISSIDIA FINAL FANTASY as a genuine entry in the FINAL FANTASY series."
Does this means that Dissidia is an authentic sequel of all the Final Fantasy games? (I'm asking) Because I don't know how to interpret it. By "genuine entry" they means is canon? I think I'll let it slide for now, I'll accept Dissidia as canon, I don't have any more objections.