This work aims at capitalizing advances in the field of Process Mining applied to the domain of Interactive Digital Narratives (IDN), towards the understanding of user engagement, particularly, spotting when and what happened when user engagement dropped. An online IDN system was adapted to implement an engagement sampling protocol, probing 74 users for Continuation Desire during runtime. The playtest dataset was coupled with the engagement self-reports and analyzed using Process Mining. We identified a subset of User-Initiated Actions associated with higher engagement trajectories, as well as actionable feedback for improving the system. We consider Process Mining as an asset for the evaluation of IDN systems and the characterization of the Interactive Narrative Experience.