It looks like it didn't update your Game Loader as it's still showing the previous patch of Nov 5th 2015.

What you will need to do is on your PC go to Documents -> My Games -> FFXIV and then you will see a file called FFXIV_BOOT

You need to open that file in Notepad.

You will see this

"BootVersionCheckMode 0"

you need to change it to this

"BootVersionCheckMode 1"

and then save that document and then close it.

Right Click FFXIV and click Run as Administrator and then it should run through the Version Update again and be able to patch your game.