Stress-related disorders are highly prevalent among first-year college students. Gaming disorder (GD) is an emerging disorder linked to physical and psychological consequences. We aimed to investigate the mechanism linking GD with anxiety, depression, and sleep disorders among first-year undergraduate students. Four hundred fifty-seven participants were recruited, and the survey included the Internet Gaming Disorder Scale Short-Form (IGDS9-SF), Generalized Anxiety Disorder-7 (GAD-7), Patient Health Questionnaire-9 (PHQ-9), and Pittsburgh Sleep Quality Index (PSQI). Our results showed that female students scored significantly higher than males in anxiety and depression. Furthermore, we found that depression is positively and strongly correlated to anxiety, and both are moderately associated with sleep quality. Gaming is positively related to depression, anxiety, and sleep quality. Interestingly, the health sciences tracks showed lower sleep quality than undergraduates from other tracks. There was a 64% variance in depression explained by many predictors, including anxiety, sleep quality, gaming, painkiller use, and gender. In addition, the mediation models showed that the association between gaming and depression is mediated indirectly by sleep quality, and sleep quality may be mediated directly by anxiety. The first year in college occurs at a critical developmental and professional stage, and our results highlight the need to establish support programs and conduct mental health educational workshops.