Is there a classification of all theories belonging to the string landscape with chiral gauge couplings? No, we are far from such a precise knowledge of the string theory landscape.
Nevertheless, a sample of representative approaches can be mentioned:
1) Heterotic string compactifications on Calabi-Yau: See Chiral four-dimensional heterotic strings from self-dual lattices.
2) Four-dimensional $N=1$ superconformal quiver gauge theories: See brane tillings and their applications. The simplest cases of this class of theories are dicussed in the case of local Calabi-Yau, however, they model the local behaviour of a wide class of semi-realistic theories.
3) Intersecting branes setups: See the excellent review https://arxiv.org/abs/hep-th/0502005.
4) F-theory compactifications: See the outstanding A Quadrillion Standard Models from F-theory.
5) Strings on orbifold geometries: See strings on orbifolds.
Just to mention a few.