Thank you, Dags! Good work! That diagram makes a lot more sense. It's funny that the company made a mistake in the diagram and apparently no one caught it.
I measured the resistance across the magneto terminals with the crank at rest and got about 1600 ohms, which matches up with the bell ringer. With the magneto handle turned (but not cranked) to move the contacts, I got about 147 ohms, which means the armature winding itself. It's making more sense now. When the magneto is not being cranked, it's removed from the circuit, probably just so that current from an incoming ring doesn't go through it. It's much easier to see now with the correct diagram. When you turn the magneto, the contacts are moved, putting the local bell and the phone line in a parallel circuit across the magneto.
Dave, it's good to know we weren't both going crazy!
This whole time, there was just a mistake in the original diagram!
The only thing that still kind of confuses me is what was the purpose for the normally closed contacts? It seems like the way this telephone is wired, they don't really do anything. All you would need is a simple mechanism to disconnect the magneto from the rest of the circuit when it's not in use. You only need one set of contacts. Why have two? I also don't understand what the extra screw terminal was for. Maybe that magneto was used for several different telephone models that wired the magneto differently? It's weird.