  We study the dynamics and unbinding transition of vortices in the compact
anisotropic Kardar-Parisi-Zhang (KPZ) equation. The combination of
non-equilibrium conditions and strong spatial anisotropy drastically affects
the structure of vortices and amplifies their mutual binding forces, thus
stabilizing the ordered phase. We find novel universal critical behavior in the
vortex-unbinding crossover in finite-size systems. These results are relevant
for a wide variety of physical systems, ranging from strongly coupled
light-matter quantum systems to dissipative time crystals.
