Your not doing anything wrong. Video's are always on top of everything else.

 I have added the words of a song on the slide where I have added a video,
 playing on a loop, but when the video starts, the words disappear!
 What am I doing wrong?

As Michael said, video is always on top.

Only exceptions are html and activx objects and both really need vba

You can either add text near the video or try to edit it into the video
itself. You can use free tools for this and it's not that difficult.
http://www.pptalchemy.co.uk/powerpoint_hints_and_tips_tutorials.html#video