The PC version won't feature any of the story mode as that's exclusive to Wii U. Instead, this is an online multiplayer experience.
According to developers Valhalla Game Studios:
By prior agreement with Nintendo, Valhalla has developed the free-to-play PC exclusive online game "Devil's Third Online." To spread "Devil's Third" around the world, this game service will run from September 2015 onwards, in various regions around the world following the release of the Wii U version in each region.
For Europe that Wii U release date is 28 August, for America the exact date is unknown but it will be the fourth quarter of 2015. Content will be localised for each region in co-development with regional publishers.
Devil's Third has been lurching around the development scene for a while now. Back in 2012 the game was dropped by the now-defunct publishers THQ as its profitability was in doubt. That was on the heels of a costly engine change when the company who were supplying the game's original engine went out of business.
The rights were then returned to Valhalla and the studio started talking about consoles, a PC version and their intention "to bring the Devil’s Third universe to a wide range of digital devices". They also mentioned a plan "to work with other various forms of media, including manga, novels, animation and film, to create a blockbuster franchise". It looked like the PC and tablet versions would be left to a joint venture - a collaboration between Valhalla and a company called Doobic.
A couple of years on and Devil's Third joined the Wii U lineup at E3 2014 becoming a Wii U exclusive.
More recently the game has been in the news thanks to a number of negative previews (Eurogamer's Martin Robinson brought up PS2-era visuals, camera issues and shallow combat, but acknowledged that he did keep returning to the game). Itagaki's response regarding criticism of the Wii U multiplayer option was that the Wii U's tablet controller was not recommended and that players should use a PRO controller and USB keyboard instead. More broadly he added, "At last, I was be able to understand about the reactions. Devil's Third is the game which reflects the player's skill directly/vividly. This is truth."
You can get an idea for how it looks in the trailer below: