You don’t need to subscribe to Final Fantasy XIV: A Realm Reborn to start playing it at a netcafe, you can use a registration code from the cafe to login. If you like Final Fantasy XIV you can transfer your character into a dedicated account once you are a paid subscriber and play the game at home.
Why would you want to play Final Fantasy XIV or any game in a netcafe instead of at home? Well, netcafes in Japan rent out little rooms with a PC, a chair, and unlimited soft drinks. It’s a quiet space where you can zone out in private.