As a key component of energy structure transformation, integrated energy systems effectively realise the synergistic operation of multiple heterogeneous energy sources. However, the existing studies on the optimal operation of integrated energy systems have not taken into account the system structure improvement and model refinement, which makes it difficult to fully grasp the complex interaction mechanisms and optimisation potentials within the system. In order to address this limitation, this paper proposes an optimal scheduling method for the integrated electricity-gas energy system that takes into account the dynamic characteristics of the gas network. Firstly, a two-stage P2G model and a gas network dynamic model are established by considering the two-stage P2G operation characteristics and the gas dynamic transmission characteristics. Then, the optimal scheduling model of the integrated electric-gas energy system including the two-stage P2G, gas turbine and other key equipments is constructed. Finally, the effectiveness and superiority of the proposed method in improving system energy efficiency and reducing costs are verified through simulation.