Multi-energy microgrids, such as integrated electricity-heat-gas microgrids (IEHS-MG), have been widely recognized as one of the most convenient ways to connect wind power (WP). However, the inherent intermittency and uncertainty of WP still render serious power curtailment in the operation. To this end, this paper presents an IEHS-MG model equipped with power-to-gas technology, thermal storage, electricity storage, and an electrical boiler for improving WP utilization efficiency. Moreover, a two-stage distributionally robust economic dispatch model is constructed for the IEHS-MG, with the objective of minimizing total operational costs. The first stage determines the day-ahead decisions including on/off state and set-point decisions. The second stage adjusts the day-ahead decision according to real-time WP realization. Furthermore, WP uncertainty is characterized through an Imprecise Dirichlet model (IDM) based ambiguity set. Finally, Column-and-Constraints Generation method is utilized to solve the model, which provides a day-ahead economic dispatch strategy that immunizes against the worst-case WP distributions. Case studies demonstrate the presented IEHS-MG model outperforms traditional IEHS-MG model in terms of WP utilization and dispatch economics, and that distributionally robust optimization can handle uncertainty effectively.