Oh my god the headphone jack is non-standard.
4.4mm balanced connector
Yes apparently this is a thing.
I've never had interference pickup problems with headphone cables. Balanced is completely overkill for this length of cable + current levels.
If I did have interference problems with ordinary headphone cables: that's a great diagnostic tool to tell me that something is serious wrong in this room. Like a broken transmitter (or a microwave oven with door open and microswitches defeated).
Maybe they're trying to avoid headphones pickup up >1MHz, injecting it back into the music player, rectifying it and you hearing it back? EDIT: Why am I bothering to justify this

We have EMI immune opamps for a reason.