The growing popularity of subscription services in video game consumption has emphasized the importance of offering diversified recommendations. Providing users with a diverse range of games is essential for ensuring continued engagement and fostering long-term subscriptions. However, existing recommendation models face challenges in effectively handling highly imbalanced implicit feedback in gaming interactions. Additionally, they struggle to take into account the distinctive characteristics of multiple categories and the latent user interests associated with these categories. In response to these challenges, we propose a novel framework, named DRGame, to obtain diversified recommendation. It is centered on multi-category video games, consisting of two {components}: Balance-driven Implicit Preferences Learning for data pre-processing and Clustering-based Diversified Recommendation {Module} for final prediction. The first module aims to achieve a balanced representation of implicit feedback in game time, thereby discovering a comprehensive view of player interests across different categories. The second module adopts category-aware representation learning to cluster and select players and games based on balanced implicit preferences, and then employs asymmetric neighbor aggregation to achieve diversified recommendations. Experimental results on a real-world dataset demonstrate the superiority of our proposed method over existing approaches in terms of game diversity recommendations.