Yes this works on this game too and have done this quite a few times myself (including running it on a USB drive so it works on all computers!)

You just need to copy two directories:

1) The main game directory from wherever you installed it (and everything in it). It doesn't matter where you copy this to on your new computer. It will run from anywhere.
2) The "Documents\My Games\FINAL FANTASY XIV - A Realm Reborn" directory. This must go back within your Documents folders under My Games (create if needed) on your new computer.