Docker on Linux runs in a VM? No.

Systemd docker-replacement on a non-systemd Linux would need to run in a VM, though.

Systemd-docker-replacement: works only on systemd-Linux. Tooling for any other arrangement, including non-systemd linux, left as an exercise to the user.

Docker: works on Linux—systemd or otherwise. Has tooling to making working on macOS or Windows non-terrible and lets you use (mostly) the same commands as you would on Linux.

I'm saying that cross-platform tooling is what makes Docker Docker. Systemd can't replace it without replacing the tooling, even if it can do the same thing only on systemd-Linux.