The PS4 does not use Direct3D. Sony would never give Microsoft any leverage over their platform. The graphics API the PS4 uses is called libgnm.

When people refer to Direct3d outside of the API, like towards a graphics card, they are talking about a feature set. What is the capability of the graphics card? If the card is a Directs 11 class card, then the card supports compute shaders.Compute shaders were optional in 10 but are mandatory in 11.

DirectX class is Microsoft marketing. Sony would never use Direct3D as an API on its platform.