We have used dynamic Monte Carlo simulations to assess the self-diffusivities and transport diffusivities of binary mixtures in a lattice model for silicalite as functions of hopping rates, mixture composition, and total loading. We compute binary transport diffusivities using the Onsager formalism and subsequently discuss the binary Fickian and Maxwell-Stefan diffusivities. We have used our results to examine the accuracy of several approximations to mixture transport diffusivities that have been suggested previously. Our numerical data strongly support the observation that single-component Maxwell-Stefan diffusivities in this model exactly obey a mean-field expression. Our data also show that a relationship between the binary self-diffusivities and the binary Maxwell-Stefan diffusivities that was claimed by several authors to be exact is in fact only approximate. We have similarly examined several methods that have been proposed for predicting binary self-diffusivities from single-component data.