Shale gas has played an increasingly important role in world energy supply in recent years. The gas transport process in the shale matrix is particularly important as it affects the long-term production behavior of shale gas. The shale matrix consists of inorganic minerals and embedded organic matter with mass transfer influenced by mechanical interactions. We develop a micro-scale discrete coupled model to explicitly account for mass transfer and mechanical interactions, and how these interactions affect the gas transport characteristics of both components. Specifically, the model comprises organic matter embedded within inorganic minerals. The proposed model is implemented and solved within the framework of COMSOL Multiphysics (Version 5.4). The model is first verified against the results of a desorption-diffusion-seepage coupled experiment and then extended to field scale. It is found that the impacts of gas pressure and effective strain are different for the gas seepage in inorganic minerals and gas diffusion in organic matter. Gas pressure may enhance the permeability of the inorganic phase due to the gas slippage effect while compactive effective strain decreases permeability during the gas depletion process. For gas diffusion in the organic matter, surface diffusion decreases and effective diffusion coefficient increases with declining gas pressure. While the impacts of effective strain on the effective diffusion are dependent on the external boundary conditions, the effective diffusion coefficient is lower than the initial value under constant stress conditions and larger than the initial value under constant volume conditions. The proposed model provides a complementary method to conventional continuum dual-media approaches and provides a clear understanding of the interactions between the two components. Field-observed oscillatory gas production data is readily history-matched and key mechanisms explained with the proposed approach presented in this work.