In the present study, the self-diffusion coefficient and viscosity of methane (CH4) and carbon dioxide (CO2) were studied by molecular dynamics (MD) simulations in the superheated vapor, gaseous, and supercritical state. The parameters used for the MD simulations are based on new molecular force fields (FFs), which were derived from previously developed, highly accurate pair potentials based on ab initio-calculated interaction energies in the limit of zero density. Using these optimized rigid all-atom FFs, multiple MD simulation runs in the order of several μs were performed to evaluate the dynamic viscosity from the plateau of the time integral of the pressure autocorrelation function and the self-diffusion coefficient from the linear Einstein regime. For the latter property, it is shown that the Yeh-Hummer correction accounting for effects of the finite box size for dense liquid systems in the hydrodynamic regime can be transferred consistently to gaseous systems at various densities. A comparison of the simulated dynamical properties obtained from our ab initio-derived FFs with those obtained from established literature FFs showed that our suggested approach is superior to the other rigid all-atom approaches and in particular to flexible and united-atom models over density ranges corresponding to pressures between 0.1 and 10 MPa. For temperatures of 295, 325, and 355 K, our simulation results for the product of self-diffusion coefficient and density as well as for the dynamic viscosity with average expanded statistical uncertainties (k = 2) of 0.6% as well as 8.0%, respectively, represent the density dependency of both properties and agree with the few simulation and experimental data available in the literature.