Gamification can give you influence over your users actions. This can happen over time such as people visiting X page more often because you've incentivized it or built unique content such as quests to promote it. Also influence can be instantaneous if you have built Gamification content that you can push to players instantly to give them some offer, challenge etc. Keep in mind, influence should not always be considered a bad thing. Good UI influences users. Influence also could even relate in Education to influencing students to complete their homework.
Fun is not easy to measure, but it's definitely a major benefit of Gamification. Things are generally better if they're more fun, and why wouldn't we want the entire world to be more fun, including life? The Fun Theory is worth exploring, the idea that something as simple as fun is the easiest way to change people's behavior for the better.