A digital twin model of an integrated energy system (IES) is established, incorporating an integrated energy system operator (IESO), an energy supplier (ES) equipped with carbon capture system (CCS), and a load aggregator (LA) that considers demand response. First, the IES system model is constructed, with tailored constraints for different system components and the introduction of a penalty mechanism for wind and solar curtailment. Then, an IES distributed cooperative optimal operation strategy based on a leader-follower (Stackelberg) game is adopted, and the strategy is solved by combining genetic algorithm and quadratic programming algorithm to obtain the optimal IES scheduling scheme. In this game theory framework, IESO acts as the lead player, while the CCS-based ES and the demand response LA act as followers, jointly optimize the IESO’s pricing strategy, ES contribution plan, and user demand schedules. Real-time IES data is obtained by the digital twin system. After the data of different dimensions and formats are processed and analyzed in a unified manner, the proposed method is used to optimize the IES optimal decision scheme. Finally, by using the digital twin model to obtain the basic operation data, simulation experiments based on the extended IEEE 39-node system and 6-node heating system yield IESO optimal price strategy, ES optimal output plan, and LA optimal energy use plan, leading to more economical energy supply and more rational energy consumption. The leader-follower game-based decision-making method based on a digital twin model, allows the power grid to move beyond heavy reliance on historical data, reduces extrapolation errors in decision-making, and enables a technical upgrade in IES optimization strategies.