As a potential substitute for the gradually depleted conventional oil and gas resources, shale gas is attracting increasing attention worldwide. Because of the ubiquitous nanopores in shale matrix, studying diffusion behavior of shale gas in nano-scale channels is crucial for its development, which also lays the foundation for the optimization of hydraulic fracturing, horizontal well spacing, etc. This paper focuses on shale gas diffusion behavior in organic-rich nano-slits and establishes a calculation method for generalized transport diffusivity using Darken approximation by molecular simulation (MS). The main conclusions are as follows. (1) For the whole gas, compared to its self-diffusivity which decreases monotonically with pressure, there is a break point for its transport diffusivity in each slit. It's found that the sequence of magnitudes of transport diffusivities in different pores at low pressures and that at high pressures are contrary. (2) For the bulk district (BD) in 2 nm slit, the self- and transport diffusivities don't differ much at low pressures and their discrepancy enlarges at high pressures, the deviation of which can be 2.34 times at 41 MPa. (3) The transport diffusivity of the molecules in the Knudsen layer (KL) in 2 nm slit is always larger (1.21-3.76 times) than their self-diffusivity and shows fluctuations at large pressures, other than the self-diffusivity in KL which decreases monotonically with pressure. Furthermore, the deficiencies and directions for improvements of the kinetic self-diffusion model and Knudsen diffusion model are analyzed by the data comparison and the theory background on their derivation and expressions. It is expected that this work will give new insights on the flow capacity of shale gas in nano-scale pores and contribute to a deeper understanding for shale gas evaluation and exploitation.