Student or Learner
(I am not a teacher) It is very common for songwriters to use bad grammar! This is one example. You will also hear "ain't" and many other "mistakes" when you listen to lyrics. Sometimes these words are just used because they rhyme better or because they give the song better rhythm.
In this case, "doesn't" is correct; however it doesn't have the same flow. The lesson: don't try to learn grammar from song lyrics! But they might help you pick up on many mistakes and colloquialisms.