We show that a (2+1) -dimensional discrete surface growth model exhibiting Kardar-Parisi-Zhang (KPZ) class scaling can be mapped onto a two-dimensional conserved lattice gas model of directed dimers. The KPZ height anisotropy in the surface model corresponds to a driven diffusive motion of the lattice gas dimers. We confirm by numerical simulations that the scaling exponents of the dimer model are in agreement with those of the (2+1) -dimensional KPZ class. This opens up the possibility of analyzing growth models via reaction-diffusion models, which allow much more efficient computer simulations.