This paper investigates the effects of a shared gaze visualization regarding social presence in an online competitive game setting. We investigate if the incorporation of gaze interaction among different competitive game genres would influence the perceived social presence for the players. To find answers to our research question we created an experimental setting that is based on two game genres that require strategic skills (i.e., a turn-based strategy game) and motoric skills (i.e., a real-time first person shooter). Our study findings highlight the positive influence of a shared gaze visualization on competitive play. Further, the studied game genres have a significant influence on the perceived social presence. With our findings we want to provide insights for game designers and researchers regarding the inclusion of gaze-based interaction in remote gaming settings.