Neurodivergent children with cognitive and communicative difficulties often experience a lower level of social integration in comparison to neurotypical children. Therefore it is crucial to understand social inclusion challenges and address exclusion. Since previous work shows that gamified robotic activities have a high potential to enable inclusive and collaborative environments we propose using robot-mediated games for enhancing social inclusion. In this work, we present the design of a multiplayer tangible Pacman game with three different inter-player interaction modalities: semi-dependent collaborative, dependent collaborative, and competitive. The initial usability evaluation and the observations of the experiments show the benefits of the game for creating collaborative and cooperative practices for the players and thus also potential for social interaction and social inclusion. Importantly, we observe that inter-player interaction design affects the communication between the players and their physical interaction with the game.