Against the backdrop of the global low-carbon transition, power-to-ammonia (PtA) has emerged as a pivotal direction for large-scale energy storage. Distributionally robust optimization can effectively address uncertainties in energy systems; however, traditional distributionally robust dispatch models generally suffer from over-conservatism that leads to increased operational costs, and existing PtA studies mostly focus on scenario-based adaptations of established optimization tools, lacking mechanistic and methodological innovations tailored to the electricity–hydrogen–ammonia coupling characteristics. To address these issues, this paper proposes a distributionally robust chance-constrained economic dispatch model (WMDRCC) based on the Wasserstein metric and first-order moment information, and introduces a logical mapping relationship that links hydrogen storage capacity with the operating modes of ammonia synthesis. This mechanism enables real-time optimization of the H₂/N₂ feed ratio, mitigates hydrogen source fluctuations, and avoids reactor instability and cost-ineffective shutdowns. Furthermore, by integrating Conditional Value at Risk (CVaR), duality theory, and big-M linearization, the complex robust chance-constrained problem is reformulated into a computationally tractable mixed-integer linear programming (MILP) model. Numerical results on the IEEE 33-bus system demonstrate that, compared with a distributionally robust model based solely on the Wasserstein distance, the proposed method effectively reduces system operating costs under the tested 24 h daily scenarios, while simultaneously improving renewable energy accommodation and reducing network losses, thereby providing a novel dispatch scheme for PtA systems that balances both economic efficiency and robustness.