I realize that this post is kind of long, so their is a very short summary at the bottom if you want to get the gist of what I have proved. I have also underlined the important parts. Enjoy
The inhabitants of the Kingdom of Hyrule, which is usually the main setting, believe that their world was created by three goddesses: Din, Nayru, and Farore. These three beings also respectively represent Power, Wisdom, and Courage. This immediately made me think of the Trinity in which the Father = power, the Son = knowledge, and the Holy Spirit = primal love. So now you're your thinking, " Okay, I see the connection for the first two, but what about courage and love?" Well, lucky for you, I have an answer for that as well. In the game the goddesses put all of their power into an object called the Triforce, and the pieces of this holy object are sought after and powerful. Ganondorf, who is possessed by the evil spirit Ganon, who we'll get to later, takes the piece representing power by force. The piece representing wisdom is taken by Princess Zelda, so that Ganondorf does not get all of the pieces. The last one, however, disappears for a while, and is finally bequeathed to the Link, the protagonist of the game, by the goddesses. The goddesses explain to him that he was given the power of Courage because of the love that they shared for the Kingdom and for Link himself. So, Link's power of Courage actually derives from the goddesses' love, creating the parallel to the Holy Spirit.
Now I can explain Ganondorf, or rather Ganon's, other meaning. Ganondorf desired power, specifically godly power, more than anything else and was willing to do anything to get it, even kill his own people or start a war. Ganon, a giant beast-man hybrid who envied the goddesses' power, reveals himself as the main cause of Ganondorf's desire. Lets think back to another being who questioned the all mighty and sought more power, Satan. Satan does fight a war against God but loses in the end, becoming a hulking mass of hair, hooves, and hunger. So, the game essentially depicts Satan through its main enemy, Ganondorf. But it doesn't stop there, you may remember in Milton's Paradise Lost that a certain someone came flying in on a chariot to deal the final blow to Satan and defeat him. The Son does this act, and, similarly, Link also deals the finishing blow on Ganon, sending him to "eternal imprisonment" - even thought he gets out again... Now I can get to my point, the game uses the protagonist Link to represent the Son in this scenario.
In summary, this game not only blatantly refers to the Trinity and other religious themes, but also depicts part of the great battle between Satan and his forces and those of God (Father, Son and Holy Spirit)