Good read, but "The tool that really runs your containers" isn't quite right either.
Bocker (docker runtime in ~100 lines of bash) does a good job showing what's really happening. Basically namespaces and cgroups, both of which come with Linux. The source is probably the best "deep dive" on containers I've found.
https://github.com/p8952/bocker
Docker thrives because of the repository of images, a great name, and some marketing. Runc thrives because it provides a nice wrapper around namespaces, mounts, cgroups, virtual network interfaces, etc. Neither really provides the magic, though...it's already there.