We study the nucleation of model two-dimensional crystals formed from anisotropically interacting molecules using kinetic Monte Carlo simulations and the forward flux sampling algorithm. The growth probability P(n) of a cluster of n molecules is measured while the supersaturation s and interaction anisotropy of the molecules are varied, in order to gain insight into the nucleation mechanism. It is found that with increasing degree of interaction anisotropy the nucleus size (defined as the cluster size at which P(n) = 0.5) can increase with increasing s, with sharp jumps at certain s values. Analysis of the cluster shape reveals that nucleation in the system studied is of a non-standard form, in that it embodies elements of both the classical nucleation theory and the density functional theory frameworks.