It is not very probable that only public interfaces are used to implement this subsystem. Therefore, we can think that the special exception of the GPL that exclude major components of the OS would not apply. It also explicitly won't apply in the first place because MS is absolutely in the case: "that component itself (1) accompanies the executable (2)"
I'm pretty sure you can use only public interfaces to implement this subsystem. You can do quite a lot to NT via the public interfaces, and it helps that the stuff in the linux subsystem basically only needs to work with itself (i.e. you don't need to send signals to Windows processes... but even if you needed to, you could use public interfaces to do that from the kernel...)
(1) core NT kernel (2) Linux subsystem