Gamification Server is not part of SF LMS (unfortunately).
SF LMS supports it, and can be configured to use a gamification server, either Bunchball Nitro or Centrical Pulse (the last one is the latest recommendation by SF).
When you know which tool to use, you have to purchase licenses from them, and then integrate with SF LMS.
Then you can use badges, challenges, leaderboards etc in SF LMS. But the actual engine is controlled by the provider you license up with.
Hope the above helps.
Niels Peter Johansson