You aren't giving it enough credit. The algorithm uses just a few seconds from any part of the song, and has to deal with phone audio quality and often background noise. I mean, you can be in a bar with all that jabber and hold up the phone and it could pick out the song. The app on the phone does the preprocessing to the audio before it is sent to the server that does the matching ... using the comparatively miserable power of a 2001 era cell phone.