Effective teamwork is essential in structured, performance-driven environments, from professional organizations to high-stakes competitive settings. As tasks grow more complex, achieving high performance requires not only technical proficiency but also strong interpersonal skills that allow individuals to coordinate effectively within teams. While prior research has identified social skills and familiarity as key drivers of team success, their joint effects -- particularly in temporary teams -- remain underexplored due to data and methodological constraints. To address this gap, we analyze a large-scale panel dataset from the real-time strategy game Age of Empires II, where players are assigned quasi-randomly to temporary teams and must coordinate under dynamic, high-pressure conditions. We isolate individual contributions by comparing observed match outcomes with predictions based on task proficiency. Our findings confirm a robust 'team player effect': certain individuals consistently improve team outcomes beyond what their technical skills predict. This effect is significantly amplified by team familiarity -- teams with prior shared experience benefit more from the presence of such individuals. Moreover, the effect grows with team size, suggesting that social skills become increasingly valuable as coordination demands rise. Our results demonstrate that social skills and familiarity interact in a complementary, rather than additive, way. These findings contribute to the literature on team performance by documenting the strength and structure of the team player effect in a quasi-randomized, high-stakes setting, with implications for teamwork in organizations and labor markets.