It's properly called Litz wire but I've been calling it tinsel wire for years. Nothing new, WW2 era headphones used it for flexibility, I had to replace it with zip cord on my Western Electric B29 cans. I also have a Bendix key from one but I digress.
I suppose you're right, due to compact size those portable players don't have enough output power to drive an 8 ohm load without distortion. Funny how in the days of shoulder carried boom boxes they cranked them up to the point they sounded like fuzz boxes and bopped down the street like Mister Natural truckin'. (Art Crumb and Zap Comix, Google is your friend.)
I guess being old school my idea of headphones bears no resemblance to those used on portable devices, more like broadcast and recording studios. I used headphones long before the Sony Walkman was invented. (;->)