As other have pointed out, you are obviously wrong about Microsoft Direct X being available on Sony's Playstation 4.
But you are also wrong in the larger picture. Direct3D and OpenGL are first and foremost abstraction layers to access the GPU. Since in a console the hardware is immutable, you can gain a lot of performance by skipping (or trimming the fat of) these abstractions.
The XBox 360 version of DirectX is very different from the PC version: it's much much closer to the metal and exposes pretty much all the GPU functionalities.
There's no reason to think that it will be any different for the XBox One. Hardware-wise it's a very average PC: its sole advantage versus an actual PC is this ability to get that much closer to the metal.
But you are also wrong in the larger picture. Direct3D and OpenGL are first and foremost abstraction layers to access the GPU. Since in a console the hardware is immutable, you can gain a lot of performance by skipping (or trimming the fat of) these abstractions.
The XBox 360 version of DirectX is very different from the PC version: it's much much closer to the metal and exposes pretty much all the GPU functionalities.
Here is a thread talking about XBox 360 dev: http://beyond3d.com/showthread.php?t=62049
There's no reason to think that it will be any different for the XBox One. Hardware-wise it's a very average PC: its sole advantage versus an actual PC is this ability to get that much closer to the metal.