It's windows host because it has the unique property of leaking to higher levels of abstraction and leaking to lower levels of abstraction, which is a technological feat that can only come from Microsoft.
I've ran Docker in LXC in a KVM before. I used LXC to have multiple containers on a VPS. Then I had to run something that works best with Docker, so I stuck Docker in an LXC.
Windows itself is technically running in a VM if you have Hyper-V enabled (not quite that simple, but that's a reasonable approximation). Hyper-V is a type 1 hypervisor which means it runs directly on the underlying physical hardware, and both Windows as well as any VMs you create are running on top of Hyper-V.