Oh come on, Game Freak--you weren't even trying to hide the fact that this a trio of gods! The references are a bit more subtle when these three are in their animalistic Therian forms, but in Incarnate mode, they're practically bashing you over the head with their djinn-like appearance. And while you might've assumed they were just elemental genies, Tornadus, Thundurus, and Landorus are directly analogous to Fujin, Raijin, and Inari, three spirits oft worshipped in the Shinto faith.
Kami is the Japanese word for god, spirit, or deity, who are worshipped by Shinto practitioners for a variety of reasons. But these Pokémon actually occupy multiple cultural mythologies: the Therian forms are all parallels to Four Symbols of Chinese constellations, namely the Vermilion Bird, Azure Dragon, and White Tiger. You know what? We're not sure we're comfortable with the idea of entrapping mythological deities in little orbs so we can carry them around in our pockets.