Providing customized products and services in the modern business world is one of the most efficient solutions to improve users' experience and their engagements with the industries. To aim, recommender systems, by producing personalized recommendations, have a crucial role in the digital age. As a consequence of modern improvements in the internet and online-based technologies, using gamification rules also increased in various fields. Recent studies showed that considering gamification concepts in implementing recommendation systems not only can become helpful to overcome the cold start and lack of sufficient data, moreover, can effectively improve user engagement. Gamification can motivate individuals to have more activities on the system; these interactions are valuable resources of data for recommender engines. Unlike the past related works about using gamified recommendation systems in different environments or studies that particularly surveyed gamification strategies or recommenders separately, this work provides a comprehensive review of how gamified recommender systems can enhance user engagement in various domain applications. Furthermore, comparing different approaches for building recommender systems is followed by in-depth surveying about investigating the gamified recommender systems, including their approaches, limitations, evaluation metrics, proposed achievements, datasets, domain areas, and their recommendation techniques. This exhaustive analysis provides a detailed picture of the topic's popularity, gaps, and unexplored regions. It is envisaged that the proposed research and introduced possible future directions would serve as a stepping stone for researchers interested in using gamified recommender systems for user satisfaction and engagement.