The amount of data in the globe is increasing at an exponential rate, and the role of digital technology and data elements in the modern growth of China’s sports business is becoming more significant. Disputes over sports data rights have grown in the international arena, with a special focus on how to preserve the sports data rights of key stakeholders. This study begins from the standpoint of stakeholders, constructs a tripartite evolutionary game model of the government, sports enterprises, and the public around the issue of sports data rights protection, investigates the behavioral evolutionary characteristics of each stakeholder and its stabilization strategies, simulates and analyzes the evolutionary stabilization strategies of the stakeholders in various situations using MATLAB, and proposes a compatible institution. According to the findings of this study, the cost of sports data governance, the cost of sports data sharing, the degree of sports data compliance use, the government incentive system, and the government regulation mechanism are the important elements impacting each stakeholder’s behavioral decision-making. Based on the foregoing, the study proposes corresponding institutional strategies for governments to respond to the issue of sports data rights, which will be more conducive to the safe use of data for development and humanitarian action, as well as contribute to global sustainable development.