In Steam's recent developer conference, they announced the addition of support of new controllers to the Steam API, one of which being the Dualshock 4. As usual though the hype train took off before people stopped to read the destination.
Fact is DS4 support is coming to Steam's API, not Steam (as a blanket term). Though many game support the Steam Controller through built in backwards compatibility to the XInput standard, unless games explicitly use the Steam API, the Dualshock 4 support will have no bearing. And the truth is very few games currently do use the API for controller input.
But hopefully all this will change as Steam sweetens the pot and tries to lure developers to the API by adding more controllers (more to be announced). But as of yet the Xbox 360 controller is not on the list and since this would be the main selling factor for developers, one has to wonder why and how they got the Dualshock 4 on board before the more widely used and accepted 360 controller. Licensing issues?