We used that tool often growing up and yes it works. For deep hooked fish I use a forceps and go through the gill, but this tool works very similar.
I will do my best to describe. This tool works best for when the fish has swallowed the hook but you can see the hook by pulling slightly on the line. With the fish in the net over the side of the boat or on the floor of the boat, pull the line tight with your left hand. Hold the tool like you would hold a pistol in your right hand and pull the tool back toward you along the line so the wire guard on the front grabs the line. Now the line should run up and down inside the gap on the front of the tool. Run the tool down the line and into the fishes mouth. Keep the line tight in your left hand. Ideally you will be pulling the head of the fish up off of the floor. Now point the tool straight into the fishes mouth and as far down the line as you can into the throat. Pull the trigger. You may have to do it a few times. The fishes head should fall back into the net or onto the floor and the hook should pop out and hook onto the tool. Now you can simply wiggle the hook free from the tool.
I hope that makes sense. It might sound pretty inhumane but it is effective at removing hooks and giving the fish the best chance to survive. Obviously the quicker and less handling the better.