Think that the writer meant the suite of OpenGL like languages like OpenGL ES, WebGL, etc.

GL is a pretty clear nickname of OpenGL. For example libGL and the fact that all functions start with `gl`.

It might be a Swedishism, I noticed the SE domain.

In the context of graphics programming (in my experience), the "Open" is often dropped here since it's pretty clear which API is being referred to with just "GL". Easier to say, without the forced slowness of the long "O" in "Open".

Not according to the official site: http://www.opengl.org/.

"OpenGL" is a trademark of the Khronos Group, and there are implementations, like Mesa3D, that do not have permission to use that trademark. Mesa's implementation is (somewhat jokingly) known as "MesaGL" but is definitely a reasonable and performant GL implementation. "GL" works well for referring to the graphics language without invoking the trademark.