Linux Subsystem would be completely wrong, because it is a Subsystem of Windows not of Linux.
Y of X providing Z - Windows Subsystem for Linux.
Y providing X on Z - Linux Subsystem for Windows.
The former is "for [having]", the latter is "for [use on]".
MS has some confusing naming, this isn't one of them.
While W S for L is fine in the intended sense, it could just as well mean a subsystem on Linux that runs Windows (like Vine, I guess). Parallel examples might be Brake Pads for Chevys or Oven Cleaner for Microwaves.
As further examples of the weirdness of compound nouns in English, consider Atomic Scientist, which does not mean a scientist who is atomic, but rather an 'ist' (= person) who does atomic science. Likewise Nuclear Physicist, Artificial Intelligence Researcher (at least for now, since AI systems aren't researchers :)).