No, on windows you still have to run a Linux vm which the containers will run inside. Meaning all containers actually run on a Linux host. The new Docker for Windows app only abstract away some stuff so it feels easier working with.
> does it work the other way around
No
I don't think, that's correct. To me that's the whole point of having a native Windows / Mac version of docker. From their feature list:
> Faster and more reliable – native development environment using hypervisors built into each operating system. (No more VirtualBox!)
The quoted part is that instead of VirtualBox one can use Hyper-V. In either case, it's handled by docker-machine which runs a GNU/Linux VM with Docker (host) tools installed, and containers are ran on that VM.
I would be surprised if there aren't plans to support WSL (to run Linux-targetting binaries on Windows "natively", thus have "native" Docker containers) but don't think that's available yet.