Sound powered telephones are really just intercoms with an efficient microphone and fairly efficient speaker: -
The microphone transducer converts sound pressure from a user's voice
into a minute electrical current, which is then converted back to
sound by a transducer at the other end. The most significant
distinction between ordinary telephones and sound-powered telephones
is in the operation of the microphone. Since the microphones used in
most telephones are designed to modulate a supplied electrical current
they cannot be used in sound-powered transducers. Rather, most
sound-powered telephones use a dynamic microphone. A common approach
to transducer design is the balanced armature design because of its
efficiency. The number of simultaneous listeners is limited because
there is no amplification of the signal.
A sound-powered telephone circuit can be as simple as two handsets
connected together with a pair of wires, which is defined as the
"talk" portion of the circuit. Talk circuits can be realized over a
pair of wires that are thirty miles (50 km) long. More complex
circuits include magnetos, selector switches and bells to allow one
user to select and call another, which is defined as the "calling"
portion of the circuit. The voice communication ("talk") circuit is
completely separate from the "call" circuit, allowing communication to
take place without external power.
I also remember as a kid having an intercom that I could speak with the kid next door with. It had no batteries and just two wires - speaker to speaker and when you wanted to listen you'd listen and when you wanted to speak you'd speak. No alert sounds to call the kid next door because there was no power but it works.
Like Olin says in his answer a carbon microphone altered its resistance according to air pressure (aka speech) and with a battery in series, it modulated the current to the loudspeaker at "the other end".