That's weird. It should definitely switch to the new article if you click the picture/play icon or the title. As a workaround, could you try "up/down" arrows? It's possible the HTML5 audio player in FF19 is buggy.
edit: It looks like FF19 is complaining about the content-type: "audio/mpeg" when changing articles. Not sure what one it is using, but it does manage to play the first article only.