Higher Education Instituions (HEIs) should be the driving force behind the training of college students in terms of both hard and soft skills (for example, innovation and teamwork competencies), and they should also do so without neglecting their health and well-being, perhaps more than ever in these complex times of the SARS-CoV2 pandemic. Game-based learning (GBL) could be a powerful and useful tool in this regard. There is, however, some controversy surrounding the use of games for learning purposes in higher education institutions, and most of the research done about this issue corresponds to GBL through digital games. Under this background, the main objective of this study was to test the effect of GBL on the intrinsic motivation (IM), teamwork engagement (TWE), team building (TB), teamwork competence (TWC), and innovation behaviors (IWB) of 142 college students of Health Sciences and Social Work. After rehearsing in small groups, the game was tested (T2). Our results obtained through the differential analyses confirmed that undergraduates were more intrinsically motivated, experienced more TWE, TB, and TWC, and developed more IWB than before playing the game (T1). Therefore, the development of core personal skills might be promoted effectively by games in an efficient, engaging, and motivating way.