You are using a plugin, I believe Yoast's Google Analytics plugin, that is conflicting. ITs the option in Yoast's plugin for tracking outbound links, it's messing up the javascript to play the player in the page. When javascript fails, the file is then opened in a new tab/window for the brwoser to handle the playback (this is fail over in the event of javascript not working).
This will be fixed in PowerPress next update, but you can also fix this by disabling outbound links in Yoast's plugin.