I did actually think of another way they could be wired. This would be a sound-powered arrangement, with the batteries used only for calling. It would need the microphones to be dynamic types (probably identical to the earphones) rather than carbon types. Wiring them in parallel rather than series would allow more current from the battery to the buzzer. (Either way, at most only one-third of the energy from the microphone actually makes it to the other party's receiver; one-third goes into your ear, and the remainder is wasted in the other party's mic. And that's not accounting for what gets swallowed up in line losses ..... Of course, you are speaking at full volume straight into the microphone, while they have their ear pressed tightly against the receiver; so as long as the total electrical losses are still less the inverse square law losses of sound travelling a few metres across a room, things are still pretty much in your favour.)
The left hand phone is shown with the handset on the rest. The right hand phone is shown with the handset lifted. Current flows from the called party's battery, through the calling party's handset and the called party's buzzer. When both handsets are down, the batteries are wired so they fight against one another; the voltages are equal, so no current flows. When both handsets are up, the batteries are out of circuit altogether and the only energy sources are the microphones.
At any rate, it should not be too difficult to sort out the wiring scheme inside each phone unit if you have them there in front of you.