They're wireless headphones, which didn't even exist.

I'm sure in context it's supposed to be a cassette-based Walkman or something like that and wrong. Especially given the title. BUT we did have these in the 90s and you reminded me of them: https://www.radiomuseum.org/r/sony_fmam_walkman_srf_hm55.html

There were some RF and infrared wireless headphones going back that far, but for use with a proper stereo, nothing portable.

Edit: Apparently the ones in that game are direct rip offs of the Koss Porta Pro from 1984 which were obviously wired.