The music in question is mostly rhythmic, as expressed by these two videos: Sound Jumble beginning at 39 seconds into the video, and Stomp Out Loud at 2 minutes and 57 seconds into the video. The Blue Man Group has also done this sort of music before. I've looked on other sites, but haven't found any names or genres that can be found on Spotify or Pandora.
There is body percussion, for example, creating sounds using hands, fingers, whistling, hitting cheeks or buttocks, etc.
There is beatboxing, using purely the mouth to make up sounds.
But perhaps the closest to what you are looking for is called "trash percussion" (which is what the first link above calls the music performed by Stomp). As utlimately, most of non-instrument sounds come from hitting one element to another (unless you were to use an external source of energy like wind), percussion is the broadest term to account for such genre. There are tons of youtube videos on trash percussion. This is a TEDx talks about it, including a music performance.
Notice the above is probably not a universal name, and perhaps not a genre in its strict sense, but it seems decent enough.