If you look at their tutorial video, you can see what's going on. The tutorial has a lot of commands like
ip link add wg0 type wrieguard
ip addr add 10.1.20.1/24 dev wg0
wg set wg0 listen-port 5100 private-key /etc/path/to/key
ip link set wg0 up
wg set wg0 peer........
If you look at the wg-quick script, it basically reads an /etc/wireguard/<adapter>.conf and runs the same commands based on your settings.
It's great when you're just trying to test things out. You can do a lot of stuff by hand, make sure it's working, try the conf file, enable the systemd or runit service, reboot and make sure it comes up.