Hi JimB,
I think your recollection of those old headphones is better than mine.
I only came across that system years ago on a very old boat.
It used a very tiny vaccuum tube in the headset, almost no other
components apart from the batteries required.
I think i was mistaken about it being like a walkie-talkie .....
I don't remember any microphone or switching involved at all.
It must have been just for reception, not for sending.
Which fits with what you say about cinemas (movies),
and the trailing wire that i recall may have been for a battery pack,
not an aerial at all !
And as you say, magnetic induction not radio waves, which kind of
limits the range from the sending loop to about a room or so.
I only recall them because i was so struck by the simplicity of them.
Haven't seen anything like it since.
Regards, John