Following the announcement of this title on the Xbox One and Playstation 4, discussions involving the possibility of bringing this title to the PC started to go around based on the idea that the x86 and AMD Direct3D11 spec hardware inside these consoles should allow for an easier port to the x86 PC platform.
In an interview, Tetsuya Nomura has been noted as saying the following on the possibility
"This isn't something we've really discussed, but it depends on the demand. Currently it'd require a pretty expensive PC, but if we get a lot of people in the future who want to play it with full specs, I think we can discuss supporting that."
This petition is to prove to Tetsuya Nomura and the management of Square-Enix that a PC version is desired by the PC Gaming population.
I would also like to remind all those mulling over signing that this title is being developed in a PC environment, and that as this game is targetting the PS4 and Xbox One, it won't suffer the consoleportalitus that was common with ports from the previous generation.
I have seen some questions as to why such a high number of signatures is required. Please be realistic in your expectations and keep in mind that Square Enix is NOT going to focus on a version of a game that is only likely to sell a couple of thousand copies. Half a million is infact more then likely way to low to even have SE consider it comparison to the additional money spent patching any issues post release and advertising.