Every person needs their own copy of the game for each platform they wish to play on. You can not play on the PS3 unless you register a PS3 registration code to your account. Downloading from another user on the PS3 won't change this. Doesn't matter if it's digital or installed from a disc.

FFXIV is licensed on an account basis. You can log in on any PC anywhere in the world, not just the one you installed the game on, if you have a PC registration code on your service account. You can log in on any PS3 anywhere in the world, as long as you have a PS3 registration code on your service account. Otherwise, you can not log in on that platform.

Remember: any software or video game is licensed to you, not sold. You are not paying for the disc and the software data, you are paying for the license granting you the right to use it.

As the above poster said though, you don't need to download it again. You DO need to buy it again.