You can use Docker Machine and whatever backend you want, including xhyve, VirtualBox, and VMware Fusion, and enable nested virtualisation in the created machine.
hyperkit is a fork of xhyve, plus stuff like bridges between inotify and kqueue/fsevents, or transparent tcp port forwarding.
Hypervisor.framework is an API to execute hypervised code, to build virtualisation engines that can run unprivileged; you still have to write an actual virtual machine.
I misunderstood the angle this thread was taking - I thought the OP was going to ask if the Dockered MacOS could run Docker.
I was just reading up on Rancher OS, but that’s a containerisation too far at this time in the AM.