Says "summon" not "put into play".

Battlecries?

doesn't battlecry only trigger on "played" minions?

You're right

I think I was just hopeful. I would've expected Blizz's wording to be "Put all demonds from your hand into play", rather than "summon demons.. bla bla".

To me, the intuitive use of the word "Summon" is when it's tied with coming into play as a result of the player. The intuitive use of the word "put into play" means it's coming into play from some other means. Oh well