This academic paper examines the strategic interactions between Japan, other nations, and the International Atomic Energy Agency (IAEA) regarding Japan's decision to release treated nuclear wastewater from the Fukushima Daiichi Nuclear Power Plant into the sea. It introduces a payoff matrix and time-delay elements in replicator dynamic equations to mirror real-world decision-making delays. The paper analyzes the stability of strategies and conditions for different stable states using characteristic roots of a linearized system and numerical simulations. It concludes that time delays significantly affect decision-making stability and evolution trajectories in nuclear wastewater disposal strategies. The study highlights the importance of efficient wastewater treatment technology, the impact of export tax revenue losses on Japan's strategies, and the role of international cooperation. The novelty of the research lies in integrating time-delay elements from ocean dynamics and governmental decision-making into the game-theoretical model.