It's wrong because of where the "Subsystem" is, and because you start parsing the sentence with that word.
OK, it's a "Subsystem", which is a subset of a system. What kind of subsystem? A Windows subsystem! This part of the system does Windows... and you're already wrong. The Windows part isn't what the subsystem does, it's what the subsystem is a subset of. The subsystem does Linux and it's part of Windows. Saying it's a Windows Subsystem for Linux implies it's something like WINE, only moved into the kernel, if you're old enough to remember the "personalities" concept.
An alternative explanation for anyone who's still confused: it's one of Windows's potentially many subsystems -- i.e., it's Windows's Linux Subsystem -- and hence it's the Linux Subsystem for Windows, not the Windows Subsystem for Linux.
That said, I think their interpretation was likely different: it's the =Windows subsystem that is meant for Linux, kind of like how earlier they had SUA, the (Windows) Subsystem (meant) for Unix-based Applications.
OK, it's a "Subsystem", which is a subset of a system. What kind of subsystem? A Windows subsystem! This part of the system does Windows... and you're already wrong. The Windows part isn't what the subsystem does, it's what the subsystem is a subset of. The subsystem does Linux and it's part of Windows. Saying it's a Windows Subsystem for Linux implies it's something like WINE, only moved into the kernel, if you're old enough to remember the "personalities" concept.