You can't truly link a game not bought from steam to your steam account.

Yes, you can add a non-steam bought game to your steam game list but that acts merely as a launcher for those that want to launch everything from steam. It acts completely different from the game lists of steam bought games. It won't have stuff like game time tracker and such. You won't be able to reinstall the game from steam too, should you uninstall it from your pc one day.
To add a non-steam game, at the top left of the steam window, click on games. Then, click "add a non steam game to my library".

To add FF14 to steam proper, you need to buy a new copy from steam.