As above, there is no OpenGL implementation for the PS4...
Could you simply develop in OpenGL on Linux and compile for Steam and PS4?
Direct3D 9 gets you WinXP+.
Direct3D 11 gets you WinVista+.
Direct3D 11.1 gets you Win8+.
OpenGL 2.x/3.x/4.x gets you Linux/Mac/Windows.
GNM gets you PS4.
GCM and/or PSGL gets you PS3.
GXM gets you PSVita.
DirectX 11.x gets you Xbone.
DirectX 9.x gets you Xbox360.
GLES 1.x/2.x gets you Android/iOS.
WebGL gets you HTML5.
GX gets you Wii.
GX2 gets you WiiU.
If you want a cross platform graphics API, you've got to make your own wrapper around most of the above... or you can use an existing game engine that's already done this work
And Mantle gets you AMD.
Yep. On PC.
Similarly (only slightly tongue in cheek) Glide gets you 3Dfx. PVR SGL gets you PowerVR PCX. On PC ;)