Dirt Cheap FM Radios
Dirt Cheap FM radios were a thing back then. Without further details this is an educated suspicion on what it is.
The radio was likely a simple radio that ran off of two AAA batteries and was operated independently of the machine, but built into the handle. The headphone cord was likely used as the antenna. The radio likely had digital tuning with a scan and reset button. Scan allowed you to scan the band and find the station, reset allowed you to start over at the beginning of the band.
These cheap radios were everywhere and they were given away as trinkets, sold dirt cheap, there was even a Game Boy Color version that plugged into the link cable port for power. I have posted an Alibaba link to show you an example of the ones given away as trinkets, the light is more common today, but back then it wasn't as common (and was incandescent).
https://www.alibaba.com/product-det...spm=a2700.galleryofferlist.0.0.b1803074Vqs0al