The field of Interactive Digital Narrative (IDN) aims at forging a distinctive Interactive Narrative Experience (INE) by accommodating user intervention in the generation of plot events and stories. Due to the highly generative nature of IDN systems, it is challenging to validate if a narrative engine reacted according to user input providing an engaging INE. To date, a great deal of User Research methodologies employed in the field employs pre-post task questionnaires producing global accounts of the experience. Although relevant, such methods are insufficient for examining the user-system interplay that could have led users towards a certain Engagement Trajectory, or series of self-reported values of Continuation Desire sampled during runtime. In this article, we introduce a methodology for the fine-grained evaluation of the INE from the perspective of Engagement Trajectories and report the results of a study featuring user behavior pattern discovery based on Process Mining on a dataset of playtesting traces. We were able to discover and characterize 14 Engagement Trajectories encountered by 90 users of an IDN system.We consider our methodology coupled with Process Mining as a fit general-purpose technique for analyzing the process of playing in IDN.