OpenGL is nothing more than basically a language for 3d rendering. It isn't linked to any operating system or any hardware. The graphics drivers implement it on any given system.
Valve ported games from DirectX to OpenGL. They can only use OpenGL as it exists and is supported via the drivers, they have no control over it and can't change it. The graphics drivers dictate what level of support there is - not Valve, Microsoft or anybody else, so if a game uses OpenGL in SteamOS it can use OpenGL in Windows.
An API is middle-ware.
Your Operating system connects you to your peripherals, including your screen and what you see on it, the drivers connect the operating system to your GPU, which generates what you see on that screen.
Direct X or OpenGL connects the Game or software to your GPU giving it instruction of how to render it.
Direct X does this in a very inefficient and clumsy way, causing bottlenecks, its a higher level API, it does not go directly to the GPU, instead it goes the scenic route
OpenGL is much more efficient, thats why the performance is much better.
Mantle is the same thing, and it does go directly to the GPU removing the bottlenecks and improving performance.
Mantle also does this in the same way the PS4 and xBox One API's get to their Hardware, which is not the same way Direct X gets to the Hardware, Mantle bypasses Direct X on the Desktop.
Because both Consoles use the same Hardware they access it in the same way, Mantle copies that on the Desktop, so the middle-ware on all 3 platforms are the same, but by name, and used by every Game developer making games for the PS4, xBox one and PC.
Anyway... i'm off for some dinner.