The paper presents results of a multi-year quasi-experimental study of student engagement during which a video game was introduced into an undergraduate dynamic systems and control course. The video game, "EduTorcs", provided challenges in which students devised control algorithms that drive virtual cars and ride virtual bikes through a simulated game environment. Engagement was conceptualized through the theoretical framework of flow and measured with a technique called the Experience Sampling Method. The study compared engagement and other experiential measures in the last year before the game was introduced and in the year in which the game was fully implemented for the first time. Furthermore, the investigation made attempts to find connections between in-the-moment engagement and characteristics of students and situational factors. Finally, the study compared enrollment rates into an advanced level dynamic systems and control course across years, comparing the percentage of students taking the game-based course who chose to pursue the subject further to that of students who took the course without the game.