The old 1.0 European Collector's Edition had a 'making of' DVD that showed the old (Tanaka, pre Yoshi-P) development team and the FFXIV development offices, including the old server hardware! A funny thing featured is it showed one of the artists showing off a character model from the game he had literally just completed, which was Titan - ironic then that Titan was dummied out of 1.0 along with Leviathan (due to the Japanese earthquake in 2011 SE felt it was too insensitive to feature Primals that used earthquakes and tsunamis in the game after such a disaster), and thus it never actually was used.

Other than that, there are videos released on SE's official Youtube channel I think that give a look behind the scenes as well, but I think they're more general and not limited to the FFXIV team specifically.