Recent investigations show that minimal interactions of particles can give rise to complex emergent structures. In particular, complex crystalline structures can be assembled from anisotropic colloids exclusively via entropic excluded-volume interaction. These emergent interactions can be quantified and explained via directional entropic forces (DEFs). Here we study the emergent arrangement in a much simpler system of finite density lattice dimers. We propose a new computational paradigm based on tensor network contraction that does not rely on Monte Carlo sampling. Computing DEFs for the dimers with this method poses new types of questions in study of lattice models in statistical physics. We indicate the ways in which tensor networks can serve as a new graphic language to discuss rigorous computations in statistical physics.