Just after boot:

● darkstat.service - LSB: start darkstat monitoring system at boot time
   Loaded: loaded (/etc/init.d/darkstat; bad; vendor preset: enabled)
   Active: active (running) since Wed 2019-09-04 15:56:16 CEST; 2min 30s ago
     Docs: man:systemd-sysv-generator(8)
  Process: 859 ExecStart=/etc/init.d/darkstat start (code=exited, status=0/SUCCESS)
   CGroup: /system.slice/darkstat.service
           └─970 /usr/sbin/darkstat -i eth0 -p 666 --chroot /var/lib/darkstat --pidfile /var/lib/darkstat/darkstat.pi

Sep 04 15:56:14 colm.tk systemd[1]: Starting LSB: start darkstat monitoring system at boot time...
Sep 04 15:56:14 colm.tk darkstat[859]:  * Starting darkstat network daemon : darkstat
Sep 04 15:56:16 colm.tk darkstat[859]:  * done
Sep 04 15:56:16 colm.tk darkstat[859]:    ...done.
Sep 04 15:56:16 colm.tk systemd[1]: Started LSB: start darkstat monitoring system at boot time.

So yes, it does start at boot.

And now it starts with "start" too:

root@colm:~# systemctl stop darkstat
root@colm:~# systemctl status darkstat
● darkstat.service - LSB: start darkstat monitoring system at boot time
   Loaded: loaded (/etc/init.d/darkstat; bad; vendor preset: enabled)
   Active: inactive (dead) since Wed 2019-09-04 15:59:49 CEST; 3s ago
     Docs: man:systemd-sysv-generator(8)
  Process: 1877 ExecStop=/etc/init.d/darkstat stop (code=exited, status=0/SUCCESS)
  Process: 859 ExecStart=/etc/init.d/darkstat start (code=exited, status=0/SUCCESS)

Sep 04 15:56:14 colm.tk darkstat[859]:  * Starting darkstat network daemon : darkstat
Sep 04 15:56:16 colm.tk darkstat[859]:  * done
Sep 04 15:56:16 colm.tk darkstat[859]:    ...done.
Sep 04 15:56:16 colm.tk systemd[1]: Started LSB: start darkstat monitoring system at boot time.
Sep 04 15:59:48 colm.tk systemd[1]: Stopping LSB: start darkstat monitoring system at boot time...
Sep 04 15:59:48 colm.tk darkstat[1877]:  * Stopping darkstat network daemon : darkstat...
Sep 04 15:59:49 colm.tk darkstat[1877]:  * stopped
Sep 04 15:59:49 colm.tk darkstat[1877]:    ...done.
Sep 04 15:59:49 colm.tk systemd[1]: Stopped LSB: start darkstat monitoring system at boot time.

root@colm:~# systemctl start darkstat
root@colm:~# systemctl status darkstat
● darkstat.service - LSB: start darkstat monitoring system at boot time
   Loaded: loaded (/etc/init.d/darkstat; bad; vendor preset: enabled)
   Active: active (running) since Wed 2019-09-04 16:00:33 CEST; 2s ago
     Docs: man:systemd-sysv-generator(8)
  Process: 1877 ExecStop=/etc/init.d/darkstat stop (code=exited, status=0/SUCCESS)
  Process: 1992 ExecStart=/etc/init.d/darkstat start (code=exited, status=0/SUCCESS)
   CGroup: /system.slice/darkstat.service
           └─1998 /usr/sbin/darkstat -i eth0 -p 666 --chroot /var/lib/darkstat --pidfile /var/lib/darkstat/darkstat.p

Sep 04 16:00:33 colm.tk systemd[1]: Starting LSB: start darkstat monitoring system at boot time...
Sep 04 16:00:33 colm.tk darkstat[1992]:  * Starting darkstat network daemon : darkstat
Sep 04 16:00:33 colm.tk darkstat[1992]:  * done
Sep 04 16:00:33 colm.tk darkstat[1992]:    ...done.
Sep 04 16:00:33 colm.tk systemd[1]: Started LSB: start darkstat monitoring system at boot time.

Well, I could swear it was not starting before the boot and I don't know what has possibly changed.