  We investigate the superfluid properties of two-dimensional driven Bose
liquids, such as polariton condensates, using their long-wavelength description
in terms of a compact Kardar-Parisi-Zhang (KPZ) equation for the phase
dynamics. We account for topological defects (vortices) in the phase field
through a duality mapping between the compact KPZ equation and a theory of
non-linear electrodynamics coupled to charges. Using the dual theory we derive
renormalization group equations that describe vortex unbinding in these media.
When the non-equilibirum drive is turned off, the KPZ non-linearity {\lambda}
vanishes and the RG flow gives the usual Kosterlitz-Thouless (KT) transition.
On the other hand, with non-linearity {\lambda} > 0 vortices always unbind,
even if the same system with {\lambda} = 0 is superfluid. We predict the finite
size scaling behavior of the superfluid stiffness in the crossover governed by
vortex unbinding showing its clear distinction from the scaling associated with
the KT transition.
