IBM intercoms - how did they work, and how old are they?

They were connected by a piece of waxed string that had to be taut.

 

Judging by the visible circuitry you would open a circuit by lifting the earpiece off the hook and the solenoid would probably operate a buzzer. The other end picking up the earpiece would probably complete the connection, but they look like carbon granule microphones and speakers, so the quality would be poor. Around the middle of the 20th C. I'd say.
You'd need a wired connection plus a battery in the circuit somewhere.

 

Yes, same effect. It's a cousin of the old candlestick telephone, but more 'modern' and directly connected.