A poem follows a metre (can be called rhythm) and form. For example Shakespeare wrote sonnets, which is the form, and it was written in iambic pentameter (five beats per line), which is the metre. There is also free verse, which has no noticeable form or structure, but as some poets have said, that's like playing tennis with the net down.
Lyrics are the froth on top of the milkshake, and I wouldn't say they come close to poetry. There's no way Fall Out Boy are practising the same art that John Keats did.