Is this only a problem on Android phones? The screenshot he shows of the text is clearly Android. I would wonder how this would be possible on a non-jailbroken iOS device if Path wasn't left running all night.
I don't see any reports from iOS folks about this happening. It's definitely against the Android Play store TOS, though.
The Play store definitely has a more laissez fair approach to apps, but spamming like this is pretty a pretty blatant violation. Google might want to consider suspending their app.