This paper proposes a qualitative approach for identifying learners' engagement from their traces of inter- actions performed in the learning game. Learners' engagement is an effective indicator of their motivation, acceptance and attachment to the learning activity. Engagement also informs about the relevance of the content and the effectiveness of the proposed interactive learning game. Designers, practitioners and teachers need in- formation about engagement for analysing, designing and validating the learning game and also for modifying and adapting learning games in order to maintain their effectiveness. Currently, most of the approaches pro- vide quantitative information about learner's engaged-behaviours. Thus, our objective is to extract qualitative information from learners-generated data. In this paper, we propose an approach in three stages that combines theoretical works on engagement and engaged-behaviours, Activity Theory and Trace Theory. By relying on traces of interactions, this approach enables to identify engaged-behaviours in low-constraint interactive games, directly, continuously, under ecological conditions and over a long time period. Then we present the results of a user study that demonstrate the feasibility and the validity of our approach. This study has been conducted on twelve traces composed of several thousands of learner-generated data.