Apparently the headphones were around 500 ohms impedance. I guess a crystal earpiece might work as audio is derived across R2. Maybe then C5 could be deleted?
Q1 must act as a (crystal controlled) regenerative detector on RX with the level of oscillation set by R2. Not sure of RX-TX shift as this will depend on RX and TX current. There is no low pass filter either, as shown. This means harmonics will also be detected and emitted. Still, this is meant to be VERY simple. I must try it.