For those in a hurry:
The review indicates that gamification provides positive effects, however, the effects are greatly dependent on the context in which the gamification is being implemented, as well as on the users using it.
From: Does Gamification Work? — A Literature Review of Empirical Studies on Gamification (2014)
…general support for our main hypothesis that gamification is not effective per se, but that specific game design elements have specific psychological effects
From: How gamification motivates: An experimental study of the effects of specific game design elements on psychological need satisfaction (2018)
Those elements being:
Our results show that badges, leaderboards, and performance graphs positively affect competence need satisfaction, as well as perceived task meaningfulness, while avatars, meaningful stories, and teammates affect experiences of social relatedness