You then lower the bridge as per the agreement, even though you know doing so is probably damning you to hell. The Demon walks across the bridge free and leaves you to enjoy your new form that will be your true form for eternity. He knows damning you to eternity as Satyr is enough, and goes off to give his special gifts to the rest of the world.
You have doomed the world's population to the life of animals once he gets through with them, but you got your perverted desire and could care less at this point.