  We study the dynamics of vortices in a two-dimensional, non-equilibrium
system, described by the compact Kardar-Parisi-Zhang equation, after a sudden
quench across the critical region. Our exact numerical solution of the
phase-ordering kinetics shows that the unique interplay between non-equilibrium
and the variable degree of spatial anisotropy leads to different critical
regimes. We provide an analytical expression for the vortex evolution, based on
scaling arguments, which is in agreement with the numerical results, and
confirms the form of the interaction potential between vortices in this system.
