In the old versions of Docker for Windows, I remember it explicitly said it used a linux VM for the kernel.
But since the new stable version (released in July 2016 I
Docker for Windows still uses a Linux VM to run Linux containers. But instead of using Virtual Box (which is what is used with Docker Toolbox), the Linux VM is run using Hyper-V - a Windows-native hypervisor. This means that Docker for Windows ships fewer components and has less moving parts.
If you install Docker for Windows and run docker version
you'll see that the Docker Linux daemon is running on "Moby Linux".