How come Deus Ex wasn't counted? If Tomb Raider, Hitman and Thief can make your list then shouldn't Deus Ex as well?
Also, Parasite Eve should be up there too.
Any ways, I've played a majority of those games on the list in some form but Final Fantasy and the Mana series are the only ones I've played enough of.
Ion Storm (company) games covers Deus Ex.
According to Wikipedia it isn't a Square Enix franchise.