I always thought "rhythm" games involved player input needing to be timed to a particular rhythm (as in DDR, Rock Band, Guitar Hero and the like, as well as a couple of mobile games I have on my tablets - Deemo and Cytus). And a "Shmup" should require the player to actually shoot stuff in order to be a proper "shmup."
So, while I understand why the presenter uses those terms, I maintain that this game is neither "rhythm" nor "shmup."