Much like a record player's needle reads the grooves on an LP, the audio recording of tree rings are read by a computer and turned into music. The tree rings are not actually sounding musical in and of themselves (as we originally wondered when we first heard it), but rather, are being translated into the language of music.
According to livescience.com, "The custom record player takes in data using a PlayStation Eye Camera and a stepper motor attached to its control arm, and relays the data to a computer. A program called Ableton Live then uses it to generate an eerie piano track." And, that "though the record player 'interprets' rather than actually 'playing' the tree trunk, the song still vaaries with each new piece of wood."