Host a docker registry native
I take for granted you are referring to the registry server released by docker.com. The documentation clearly states on the very first line:


  Before you can deploy a registry, you need to install Docker on the host


Since the registry is the main product of the docker/distribution opensource project, you could fork and see how you can modify this as a standalone install not requiring docker, but I have no clue if it is possible and that would probably end up being a bad idea.

There are other existing products you can install 'standalone' that will let you manage your own registry. But they all come with some degree of requirements (java, ruby...). I have experience with 2 free products I use daily:


Sonatype nexus3 oss is a multi format repository manager supporting docker registries (requires java).
gitlab-ce has support for container registries in each projects if you configure it (ruby required).


The latest one is probably an overkill if you only need a basic registry and not all of the git, wiki, etc. ressources.

I recently came across a fairly recent review article listing other products I have no experience with:


Harbor from VMware
Portus by Suse


It also mentions as a bonus the use of Openshift as a registry, but even minishift for something as light as possible will require to install docker.

All of these solutions can probably meet your 'native run' requirements, but they are all much more complex to install and maintain than simply poping-up a registry:2 container.