You aim it at what you want to hear, the sound is amplified, and you listen at the other end.
Watch what the lady does as she looks over to the camera. She swings her hearing aid around to catch the sound ~ maybe someone yelling at her "Get out the way lady we're filming here".
Yes, it is a Western Electric Model 34A Hearing Aid. You can view one at http://www.hearingaidmuseum.com/gallery/Carbon/WesternElectric/info/westelect34a.htm
I’d like to see a picture of one of those hearing aids. That’s the most plausible explanation so far.