The structure of heterotic string target-space compactifications is studied using the formalism of the non-commutative geometry associated with lattice vertex operator algebras. The spectral triples of the non-commutative spacetimes are constructed and used to show that the intrinsic gauge field degrees of freedom disappear in the low-energy sectors of these spacetimes. The quantum geometry is thereby determined in much the same way as for ordinary superstring target spaces. In this setting, non-Abelian gauge theories on the classical spacetimes arise from the K-theory of the effective target spaces.