It doesn't matter at all if you write 'for', as the possession is totally unclear. "Windows Subsystem for Linux" ----- Is the 'windows subsystem' for linux?

It doesn't matter at all if you write 'for', as the possession is totally unclear. "Windows Subsystem for Linux" ----- Is the 'windows subsystem' for linux? or is the 'subsystem for linux' a windows branded feature? If you asked most people they would probably choose incorrectly.