I agree that the Rinnegan probably has unique summons, hence "Animal Realm"... I don't see the need for a summoning Path if it doesn't include summons.
I'm not saying I'm right, this is just what I think.
He summons those animals. He controlled them via the Rinnegan, which is why they all had the rinnegan in their eyes. I believe the rinnegan works in place of the contract. He is the only person I've seen that summons multiple types and forms of creatures.
Sig and Ava by Imotochan
i suspect, considering there's a bird summon with extra wings, a multiple-headed dog summon with can split after every attack, a creature summon who is part iguana part snake part some other crap lol; i come to the conclusion that these creatures are unnatural and created by the sage himself, therefore belonging to whoever possesses the rinnegan.
here's some more food to chew on: was the demon realm arguably the first puppet ever build? by the sage himself? maybe inspired future shinobi to build puppets like those form the sand village.