(1) You are running MX-Linux with systemd disabled, but sysVinit enabled.
(2) It seems during installation piaware detects this and installs sysVinit files for start|stop|restart|status.
(3) It also seems that dump1090-fa was unable to install sysVinit files, therefore it fails to start at boot, and also does not find commands sudo service dump1090-fa start|stop|restart|status .
You can manually create sysVinit file /etc/init.d/dump1090-fa similar to the step-by-step method for OpenSky feeder I have shown in the post linked below. However you will need to do some modifications in the file to make it match dump1090-fa. (I am away from my computer, so cannot tell you exactly what modificatios should be made in init.d file of Opensky. May try tomorrow morning).
Installed OpenSky Network Data Feeder on MX-Linux on Intel PC
NOTE: Two other easier alternatives
Alternative 1: Enable systemd
If you change the mx-linux’s default Grub setting to make it boot with systemd enabled, and purge+reinstall (1) dump1090-fa and (2) piaware packages after booting with systemd enabled, it will solve your problem without any modifications & workarounds.
Alternative 2: Do NOT enable systemd, use default sysVinit
This can be acheived by replacing dump1090-fa by dump1090-mutability,which installs sysVinit files by default.
sudo dpkg --purge dump1090-fa
sudo apt-get install dump1090-mutability
sudo usermod -a -G plugdev dump1090
sudo service dump1090-mutability restart