At present, China has not yet formed an effective development model for the industrialization of construction waste. The level of construction waste treatment and resource utilization is still low, and recycled products also lack market competitiveness. In order to promote the effective development of the remanufactured construction and demolition waste supply chain better, and based on the present situation, this manuscript establishes a game model for recycling units in two different situations: with and without remanufacturing capabilities. However, most existing studies have determined that all recycling units have remanufacturing capabilities. In the first situation, the main players of the game are recycling units with remanufacturing capabilities and consumers. In the second situation, the main players of the game are recycling units without remanufacturing capabilities and the third-party remanufacturer with remanufacturing ability. Therefore, our research can ascertain the optimal strategy choices of both parties in the game under different return situations and discuss the impact of changes to related parameters through numerical simulations. The results show: (1) When the recycling unit has remanufacturing capabilities, corporate leadership and government supervision rate have positive effects on its evolution to strict manufacturing. Only a high supervision rate can effectively suppress the negative impact of speculative gains and drive the system to (strict manufacturing; positive). Furthermore, the higher the supervision rate, the faster the system will converge. Then, the consumer’s payment difference coefficient has a negative effect on the evolution of the recycling unit to strict manufacturing. The larger the payment difference coefficient, the faster the system will converge to a stable state (tendency to formal manufacturing; negative). (2) When the recycling unit does not have the ability to remanufacture, the government cost subsidy rate and the recycling unit’s effort profit coefficient have positive effects on the recycling unit’s evolution to the direction of effort. Meanwhile, the larger the profit coefficient of the recovery unit’s effort, the faster the system will converge. The conclusions obtained provide certain theoretical guidance for the decision making of CDW recycling supply chain recovery units and relevant government departments.