There are 2 ways to install the game: one is via the disc and the other is via the code included in the case that the disc comes in (as well as the digital stand-alone version).

But, if you want to play the actual game, the code, which also functions as a download code, must be registered to the PSN account that is going to be used to access FFXIV (which should also be linked to your SE account).

In the end, you need to purchase the game again, either in a physical format (disc) or digitally on PS Store. However, you can use any disc to install the base game faster and then start-up the client and download the patches when you login.