The difference between 1970's and the early 90's is the Walkman. Personal, portable stereos wasn't a proven technology 30 years ago, it was 15 years ago. These "uuh, the future" TV-shows usually predict the future in terms of extrapolating current popular technology, sort of the guys Henry Ford said would have told him to make a really good horse carriage.

Looking at the (cassette-tape) Walkman and extrapolating beyond the limitations into an MP3-player device isn't very rocket science. Making it a marketable product is (almost).