Stress is currently one of society's dominant health problems with far-reaching effects on human health. Traditional methods of stress therapy are expensive and have low adherence levels. There is growing research in the area of biofeedback (BF) games, in order to provide cheaper and more engaging alternatives. In our previous work, we presented three BF games, and showed how these games helped manage stress better than traditional stress therapy activities, like Paced Breathing. Given the crucial role engagement can play in determining the effectiveness of learning stress self-regulation in our biofeedback games, in this paper we investigate how best to quantify engagement physiologically. To achieve this, we pursue two main goals: 1) provide a framework for evaluating player engagement, and 2) develop machine learning models to predict levels of engagement during these stress therapy activities. Our main contributions are to present a metric for engagement based on physiological profiles, provide a benchmark for engagement levels and present a combination of evaluation criteria to determine if a BF game session was Highly Engaged (HE) or Poorly Engaged (PE). Additionally, for each evaluation criterion, we build a Support Vector Machine (SVM) to predict if the BF game session can be labelled as HE or PE. Our work, especially relating to levels of engagement, can easily be generalized to analyzing other physiological profiles using breathing rate and Heart Rate Variability (HRV).