Animation, Puppetry, Film and TV are all mediums of entertainment, but they're also art forms.
Genre is something such as comedy, drama, action, etc. However, in film and TV when a genre is picked for it, if it's live action, then they just have to call it a comedy or drama. However, if it's animated, they would probably call it an "animated comedy/drama." If puppetry is involved, it's taken as a live action film, with no mention of puppetry.
So, all in all, while they really are mediums and art forms. I do feel that since animation is considered to be a genre by many, puppetry should be included on that, but at the same time, make it known as an art form, which is what animation should do as well.
At least, that's I hope happens. I plan to do that as a filmmaker.