He doesn't have to have finished every single FF. He's a working adult and already was when most FFs came out. Not everybody has the time to spend 60h playing one game and you would be surprised how few game directors even play their own games to completion. As a game director he should, however, at least understand what's happening in the gaming world and play the biggest titles a bit to get a feeling for the changing tastes and not to stay behind the times. And he apparently does that when you read interviews with him showing that he knows and understands current trends and development methods, especially the difference between Japanese and Western studios' approach.
He's the right guy for this series. Passionate about creating an impressive, modern FF that still knows its roots, but also open to change, trying to carefully assess what tradition-baggage really is still necessary.
See this recent, great interview:
http://www.gamesradar.com/final-fantasy-xv-how-you-make-very-new-game-very-old-series/