In the fantasy game how does Ender defeat the snake rug?

Ender returns to the game and enters the castle room at the End of the World. This time he kisses the snake on the mouth instead of killing it. It turns into Valentine, and when they touch the mirror together, the wall parts and allows them through. He thinks that "wherever he went in this world, Valentine was with him." He is distressed that the snake was Valentine all along while he kept killing it.