Ignition 101, he eliminated the magneto (what made the electricity) and kept the great coil (the hardest, heaviest, and most expensive part at the time). So a battery provides electricity and the magnet on the hub with its hall sensor provides a signal to the electronics to time the spark.
You can do what ever you want. Keep it and use it (if it still works). replace it with a new unit (which may require you to invent a bracket for a new hall sensor.
I am on the fence on this one myself, I love this old stuff.
There is a lot to say about the new stuff too.
Your photos are a little dark, but, I see nothing missing or cut off. The hall sensor has standard color coded wires. White for signal, red for +5v and black for ground.
Good luck with your little Zenoah, I have a 20cc with over 900 hours on it. I flew the snot out of it just an hour ago.