In order to improve the energy efficiency and economic effect of conventional diesel-powered rubber-tired gantry (RTG) cranes in container terminals, various hybrid RTG cranes were studied. However, these current hybrid RTG cranes have several disadvantages, such as high initial investment cost and poor versatility of energy management methods. In this paper, a hybrid RTG crane consisting of a small-sized diesel generator (DG), a ternary material lithium battery, and a supercapacitor (SC) is studied, and a hybrid RTG crane energy management method based on game theory is proposed. The DG, lithium battery, and SC are modeled as three independent agents to participate in the game, and a multi-agent system (MAS) is established. During the RTG crane work process, agents achieve a coordinated and stable working state through the game, i.e., the Nash equilibrium. Three typical crane operation scenarios, the rated load, continuous work, and intermittent work, are simulated and studied. According to the results, combinations of the three devices can meet the power demand and system performance. The power of the DG in the hybrid system is small (only 20 kW), reducing fuel consumption and overall emissions during RTG crane operation.