Smart Construction Sites (SCS) are important drivers for the construction of high-quality development. In order to determine the evolution of SCS advancement systems, an evolutionary game model consisting of government, enterprises and projects was constructed. The experimental simulations were performed by using a system dynamics approach. The findings were as follows: (1) There are three stable equilibrium strategies in the evolution of the game system: government, enterprises and projects all adopt positive strategies; government intervention, enterprises’ advancement, and projects’ non-participation; and government intervention, enterprises and projects adopting negative strategies. (2) Government penalties and balance of interests between enterprises and projects are the main factors affecting the evolution. (3) In the state (1,1,1), the influence of a government regulatory system is more significant in encouraging enterprises to promote SCS and projects to participate in building an SCS platform. (4) Government rewards and penalties, costs and benefits of corporate support for SCS, benefits when projects do not participate in SCS, are the main factors influencing the adoption of proactive strategies by companies and projects, and there are significant differences in the strategic directions and marginal impacts of each factor on stakeholders’ choices. These findings provide a reference for further refining stakeholder theory and for promoting the sustainable development of SCS.