When I first read about this feature I saw it as: SE was gonna implement a way to launch the FFXIV.exe multiple times(and have them all running at the same time) on one PC w/o using a third party app. So you would still need to buy the game three times to get the product code(maybe purchase the product code only at a discount from SE store), then link all product codes to one SE account. Then use the official Square Enix feature to launch all three game clients at the same time on one PC.

Given the rough launch SE is faced with at the moment, this sort of thing may not be implemented or clarified for a few weeks.