I would say yes, it's still self-hosting. It's probably not "home labbing", but it's still you responsible for all the services you host yourself, it's just the hardware which is managed by someone else.
Also don't let people discourage you from doing bare-metal.
No, I actually think that is a good analogy. If you just want to have something up and running and use it, that's obviously totally fine and valid, and a good use-case of Docker.
What I take issue with is the attitude which the person I replied to exhibits, the "why would anyone not use docker".
I find that to be a very weird reaction to people doing bare metal. But also I am biased. ~30 Internet facing services, 0 docker in use ๐