Ok so I got it working finally. As I thought, in my attempt to fix the button configuration (and the fact it doesn't work!) I accidentally removed all the bindings.

If you want to play FFXIV with Dualshock 4 open up your FFXIV.cfg file (default location: (C:\ ... Documents\My Games\FINAL FANTASY XIV - A Realm Reborn") with a text editor and replace every instance of "Alias {.......}" with the code below.

Alias {90,91,88,89,41,40,32,33,73,72,48,49,3,2,1,0,4,6,10,5,7,11,9,8}

Obviously the part that says Antialiasing doesnt count. Do not try to configure it through the in game settings, it will not work, and you might end up completely unbinding the whole thing (I think I clicked "skip" on all the steps).