The "container" is the first process, which can create children that inherit the same properties.

Generally this is not what Docker containers are 'for', right? Docker is intended as a system for 'application containers', which yes, may spawn child processes, but are generally not expected to include a process supervisor or service management layer internally.

Contrast this to 'operating system containers' which are designed to run an init system, so individual containers are intentionally multiprocess. Many virtual private servers run in containers of this kind, e.g., by OpenVZ.

On that note, how come you've gone with Docker for this rather than something like LXC or OpenVZ, which are ostensibly designed for the large, multiprocess container use case?

Well, they could also just mean their service is a multi-process program (as opposed to threads, which...are also processes), but it's not super clear.

see my reply above

Yes I run an init system that starts multiple processes and services. All in a Docker container.

I would be very keen to understand why LXC is better than Docker for this. I've also read this kind of "marketing" around so called "operating system containers" but I am still clueless why they are better. Concretely, what are the benefits?