yes. and no.
Did you test it after removing it from the old track?
The base of the magnet can be connected to the outside rail jumper bar on the bottom of the track. That's the common or ground.
Then, a hot wire to a button or momentary toggle and then to the coil wire. The coil wire doesn't look healthy. It looks like the end that connects to common or ground is not connected. if there is two little pieces, one would connect to the magnet plate. The other would receive the hot wire from the switch.
I would also solder a jumper wire to connect the cut in the center rail.
Use some alligator clip jumpers to test it before soldering.