The widespread use of e-bikes has facilitated short-distance travel yet led to confusion and safety problems in road traffic. This study focuses on the dual characteristics of e-bikes in traffic conflicts: they resemble pedestrians when interacting with motor vehicles and behave like motor vehicles when in conflict with pedestrians, which raises the right of way concerns when potential conflicts are at stake. Using the Quantal Response Equilibrium model, this research analyzes the behavioral choice differences of three groups of road users (vehicle-pedestrian, vehicle-e-bike, e-bike-pedestrian) at right-turn-on-red crossroads in right-turning lines and straight-going lines conflict scenarios. The results show that the behavior of e-bikes is more similar to that of motor vehicles than pedestrians overall, and their interactions with either pedestrians or motor vehicles do not establish a reasonable order, increasing the likelihood of confusion and conflict. In contrast, a mutual understanding has developed between motor vehicles and pedestrians, where motor vehicles tend to yield, and pedestrians tend to cross. By clarifying the game theoretical model and introducing the rationality parameter, this study precisely locates the role of e-bikes among road users, which provides a reliable theoretical basis for optimizing traffic regulations.