It wasn't just a case of developing an algorithm that could in theory be used to match an audio signal against all the world's pop songs. They presumably also had to get hold of a substantial number of those songs, fingerprint them, and roll out the search robustly against generally very poor audio hardware using simple telephony services at (for the time) quite considerable scale. They did it very quickly, it worked super well from launch, and it's been running continuously ever since.
I've read the paper about the method, but I would love to know more about the original development and deployment.