This paper addresses the increasingly tight energy coupling in urban energy systems, which are composed of the power distribution network (PDN), the transportation network (TN), and the gas distribution network (GDN). A non-cooperative game optimization model for the urban energy system is developed, to achieve coordinated optimization among these three different energy networks operated by independent stakeholders. To avoid excessive sharing of private information, an inner-outer iterative method is further proposed to obtain the Nash equilibrium and enhance solving efficiency. In the proposed method, each energy network is iteratively optimized by exchanging only the price and load information, and the network parameters are not disclosed. In the inner layer, the PDN-TN coupled subsystem and the PDN-GDN coupled subsystem are solved separately. In the outer layer, interactions between charging loads and gas prices are coordinated through the PDN, thereby enabling cross-network coordination of urban energy systems. Case studies demonstrate that the convergence speed of the PDN-TN coupled subsystem is significantly improved by dynamically adjusting the electricity price based on sensitivity coefficients. Balanced resource allocation of the urban energy system is achieved through the non-cooperative game, while autonomy of all stakeholders is preserved. Energy procurement costs are reduced by up to 25.56% compared with that of the PDN-TN coupled subsystem.