The Amazon wire antenna is a simple "rabbit ears" dipole with no gain. It works fine with a high quality home stereo receiver but not with a cheap FM radio.
It's simply what I described above - a crude dipole - but without a balun (which would improve it somewhat). In fact, it's pretty well identical to what we used to make when setting things up for customers, a bit of speaker wire, pull it apart to the length of your arms, fit a coax plug on the end - and they want $8.99 + expensive postage?
However, they work just as well on a cheap stereo as an expensive one - if the stereo is crap, then it's not the aerials fault - in fact many stereos come with that same basic wire aerial, and often a (much more useless) AM loop aerial.