The best thing you should take from game design in terms of how to improve work is the difference between extrinsic and intrinsic reward. Most gamification focuses on extrinsic rewards such as leaderboards, levelling and achievements. But really they should think about the intrinsic rewards of work and how to improve those. Doing the latter without the former is just running people on a treadmill towards burnout. Focusing on extrinsic rewards also has a lot of negative consequences more generally. People focused on them as individuals often do so to the detriment of the wider organisation. You see that with bonuses as well. And extrinsic rewards can result in lower creativity, less intrinsic motivation and even less satisfaction from social rewards.
Basically do the hard thing and make the work inherently better rather than the easy thing of adding hoops to jump through.