Human-machine communication has evolved from one-to-one relationships to multi-agent systems where the relationship between machines themselves influences perception and behavior. These multi-robot systems are hard to study due to the large number of emotion variables used by humans in social systems. To investigate Robot-Robot-Human interaction in a rule-based system, we developed robotic arms that narrate a human interest story using the rules of the game that the robots play. This intervention allows us to study human perception of single robot behaviors and robot-robot relationships during contexts of audience interaction. Two robotic arms are pit against each other in a game of chess, while expressively making gestures like thinking, examining, hesitating, shows of satisfaction and bewilderment, breathing, etc. These nonverbal behaviors signal to audiences emotion-like responses to the game. The rules can change between games, giving narratives of power struggles between the robots. To address behavior design for public perception, we used videos to assay audiences on interpretation of individual robot movements and how robot-to-robot expressions lead to perception of gameplay. We found that gestures like standing and confirming were perceived as aggressive, while head turns, deliberation, and audience alerts were perceived as curious. Moreover, human observers' perception of robot play style, and to some extent, their own play strategies were affected by robot-robot interaction, preferring to hold defensive strategies when the robot was aggressive, for example. Particular nonverbal expressions used by the robots led audiences to attribute personality characteristics to them, modifying their intended strategy of play in complex patterns such as pretending to be friendly first to lull the curious robot opponent while adopting an aggressive strategy.