This paper investigates the players' gaze behavior in different game difficulty settings to explore potential use cases of gaze-informed design interventions for future research activities. A comparative study was set up where subjects played the game Pac-Man in three difficulty settings while their gaze behavior was recorded via an eye-tracking device. Several measures were employed, such as the current position of the players' gaze, the current position of the Pac-Man character, and the currently attended game object. While some game aspects did not show any significant results (e.g., the distance between Pac-Man and the gaze point), the time spent looking at one of Pac-Man's enemies revealed a highly significant effect for the difficulty level. With the findings, we aim at informing designers and researchers regarding the pitfalls of using gaze as an analysis tool in the field of challenge in games. Furthermore, the insights of our efforts provide the basis for our future research activities that will use the obtained data to provide player guidance and support players in challenging game situations through visually augmenting objects located in the peripheral visual field.