Analysing and monitoring users' engaged-behaviours continuously and under ecologically valid conditions can reveal valuable information for designers and practitioners, allowing them to analyse, design and monitor the interactive mediated activity, and then to adapt and personalise it. An interactive mediated activity is a human activity supported by digital interactive technologies. While classical metric methods fall within quantitative approaches, this paper proposes a qualitative approach to identifying users' engagement and qualifying their engaged-behaviours from their traces of interaction. Traces of interaction represent the users' activities with an interactive environment. The basis of our approach is to transform low-level traces of interaction into meaningful information represented in higher-level traces. For this, our approach combines three theoretical frameworks : the Self-Determination Theory, the Activity Theory and the Trace Theory. Our approach has been implemented and tested in the context of the QUEJANT Projet. QUEJANT targets the development of a system allowing the actors of Social Gaming to analyse players' engagement from an analysis of their activity traces. In order to demonstrate the feasibility of our approach, we implemented the whole process in a prototype and applied it to 12 players' interaction data collected over four months. Based on these interaction data, we were able to identify engaged and non-engaged users and to qualify their types of engaged-behaviours. We also conducted a user study based on a validation of our results by experts. The high prediction rate obtained confirms the performance of our approach. We finally discuss the limitations of our approach, the potential fields of application and the implications for digital behavioural interventions.