Why won't docker daemon start in rootless mode?

Question

Docker

Good day!
Linux Mint 19

Installed docker in rootless mode. Everything is according to the instructions, all the necessary files are in place. I try to run:
$ systemctl --user start docker
I get:

Failed to start docker.service: Unit docker.service not found.

File

~/.config/systemd/user/default.target.wants/docker.service

in place.
What's wrong?