Are you fluent in Japanese, and have you played the Japanese versions? The "Dark World" is called "Makai" in Japan, and Ganon is a class of being known specifically as a "Maou" and his monsters are his "Mazoku." IIRC other terms such as the ones used for the Sacred Realm, "Shrine Maidens," etc. are directly taken from Japanese cultural concepts.

The English versions won't reference Shinto because they're localized for North American/European audiences, who by and large do not practice and would not understand references to Shinto.