Experiments designed to investigate the transition to non-collisional behavior in D3He-gas inertial confinement fusion target implosions display increasingly large discrepancies with respect to simulations by standard hydrodynamics codes as the expected ion mean-free-paths λc increase with respect to the target radius R (i.e., when the Knudsen number NK=λc/R grows). To take properly into account large NK's, multi-ion-species Vlasov-Fokker-Planck computations of the inner gas in the capsules have been performed, for two different values of NK, one moderate and one large. The results, including nuclear yield, reactivity-weighted ion temperatures, nuclear emissivities, and surface brightness, have been compared with the experimental data and with the results of hydrodynamical simulations, some of which include an ad hocmodeling of kinetic effects. The experimental results are quite accurately rendered by the kinetic calculations in the smaller-NK case, much better than by the hydrodynamical calculations. The kinetic effects at play in this case are thus correctly understood. However, in the higher-NK case, the agreement is much worse. The remaining discrepancies are shown to arise from kinetic phenomena (e.g., inter-species diffusion) occurring at the gas-pusher interface, which should be investigated in the future work.