This paper proposes a multi-agent evolutionary game model that can be used to study sustainable ecotourism development in national parks, with a focus placed on coordinating the interests of multiple stakeholders. Based on the limited rationality hypothesis, this study explores the impact of strategic choice evolution and the change of key factors on the stability of the ecotourism development system in national parks. To achieve this, a tripartite evolutionary game model involving “local government–tourism enterprises–tourists” is constructed. The model is applied to Wuyishan National Park as a case study, incorporating actual data and conducting numerical simulation experiments using MATLAB software. The findings of the study are as follows: (1) The optimal stable strategy for the three game players (local government, tourism enterprises, and tourists) is determined to be one that works to “supervise, implement high-level services, and participate in ecotourism”, respectively. This strategy is influenced by factors such as government subsidies, government fines, economic benefits obtained by tourism enterprises at different service levels, and the utilities experienced by participating and non-participating tourists in national park ecotourism. (2) Government subsidy policies can promote the attainment of a stable state for tourism enterprises and tourists. However, excessive subsidies may hinder the fulfillment of local governments’ expectations. (3) The greater the economic benefits obtained by tourism enterprises through high-level services are, the more favorable it will be for tourism enterprises to reach a stable state. However, this may lead to a relatively slower response from the government. (4) The higher the utilities that tourists derive from high-level services in ecotourism are, the faster the game players will reach a stable state. (5) The higher the utilities associated with tourists spending time in other places are, the more challenging it becomes for the three game players to achieve a stable state. This situation may cause tourists to shift from the initial strategy of “participating in ecotourism” to “not participating in ecotourism”. Based on these findings, the paper provides countermeasures and suggestions for promoting the sustainable development of ecotourism in Wuyishan National Park. These recommendations aim to offer decision-making references for enhancing the development of ecotourism in national parks across the country.