It's a Windows subsystem[0] for [running] Linux [applications].

The terminology is "Windows subsystem for [target environment]" so "Windows subsystem for OS/2" lets you run OS/2 application on NT, "Windows subsystem for Win32" lets you run Win32 applications on NT, and "Windows subsystem for Linux" lets you run Linux applications on NT.

[0] "The interface between user mode applications and operating system kernel functions […] There are four main environment subsystems: the Win32 subsystem, an OS/2 subsystem, the Windows Subsystem for Linux and a POSIX subsystem."

Yet they chose different terminology for WoW64 (Windows 32-bit on Windows 64-bit), and chose to store 32-bit binaries in the WoW64 directory.

I don't know that Win64/WoW64 is a separate subsystem. I think it's a subset of the 64b version of the Win32 subsystem.

The Architecture of Windows NT page on Wikipedia has a good diagram to help visualize NT subsystems. The first few versions of NT, iirc, shipped with the OS/2 subsystem but this was removed with Windows XP.

https://en.wikipedia.org/wiki/Architecture_of_Windows_NT

It's confusing, but accurate. It's a subsystem of Windows ("Subsystem" is a well-defined term in Windows land, the win32 API is o its own subsystem as well).

I wish they had promoted the name lxss more, though. It's short, very googlable, and it's the internal name.

The git repo name is even more ridiculous: https://github.com/Microsoft/BashOnWindows

(after all, I had bash on windows for years already)

I suppose it might be named that way due to trademark conserns.

Naming something as "X for Y", where "Y" is a trademark owned by someone else is often done, but I haven't seen "Y for X".

Just speculating.

I was also confused by their ancient product "Windows Services for UNIX", which does not run on Unix.

https://en.wikipedia.org/wiki/Windows_Services_for_UNIX

Microsoft also has an Android emulator for Windows.[1] One would think that would run into licensing problems.

[1] https://www.visualstudio.com/vs/msft-android-emulator/

Sorry but I'm not sure I understand your point?

Android is Apache 2.0 with the Linux / GNU parts retaining their respective GPL licence. Microsoft are distributing the OS for free, which is allowed within the terms of Android's licencing and something that is done by many other organisations including Google themselves.