Game-theoretic methods play a vital role for characterizing interactions among self-interested heterogeneous agents, and enhancing decision-making efficiency in embodied intelligent systems. This work reviews the research progress of embodied intelligent games with applications in many areas such as intelligent transportation, aircraft confrontation, and active perception games. In particularly, it explores how current research integrates classical game models with artificial intelligence (AI) methodologies to address the bidirectional feedback between cognitional space and physical space of embodied systems. First, within the framework of mathematical game models, we provide a theoretical foundation for embodied interactive decision-making. Then we discusses typical applications of embodied games from the perspectives of geospatial dimensions and task types. Subsequently, we discuss key challenges in solving embodied games, including opponent intention recognition and equilibrium computation under uncertain information, followed by a comprehensive survey of existing resolution methods. Finally, we discuss future trends in embodied game-theoretic approaches, particularly their potential and challenges in technological developments and practical applications.