We study hard-core dipolar bosons on a square lattice subject to a unidirectional periodic drive that Floquet-engineers anisotropic hopping. Driving along one lattice direction provides a controlled way to suppress transverse tunneling, yielding a kinetically quasi-one-dimensional regime with strongly anisotropic transport within the leading-order high-frequency Floquet effective description. In this limit, the system does not reduce to decoupled chains, because the long-range in-plane dipolar interaction remains isotropic and couples different chains. Focusing on dipoles polarized perpendicular to the plane, for which the interaction is purely repulsive and isotropic, we use sign-problem-free worm-algorithm quantum Monte Carlo simulations to map the half-filling phase diagram versus kinetic anisotropy and dipolar coupling. We find that increasing kinetic anisotropy systematically lowers the interaction strength required to stabilize checkerboard order, demonstrating that Floquet-induced suppression of transverse motion enhances density ordering. Near the superfluid–checkerboard boundary, the concurrent sharp loss of stiffness and growth of checkerboard correlations, their size-dependent sharpening, and the histogram analysis support a weakly first-order transition rounded by finite-size effects. Away from half filling, on the doped sides of the checkerboard plateau, our finite-size data support a narrow checkerboard-supersolid regime with simultaneously finite checkerboard correlations and superfluid stiffness, where the superfluid stiffness is anisotropic but the density pattern is isotropic.