The Kardar-Parisi-Zhang (KPZ) equation is a paradigmatic example showing universal scaling behavior out of thermodynamic equilibrium. Its universality is underlined by the diversity of physical systems which exhibit KPZ scaling, ranging from the growth of crystal interfaces, over the combustion of paper, to the growth of bacterial colonies. Recently it has been noted that also the long-wavelength fluctuations of the phase of driven-dissipative condensates such as exciton-polaritons map to the KPZ equation. However, a crucial difference between the height of a crystal interface and the phase of a condensate is that the latter is compact and may hence contain vortices. Here we discuss how vortices can be incorporated in the KPZ equation by moving to a dual description in terms of non-linear electrodynamics. In this description, the Kosterlitz-Thouless transition in a 2D condensate corresponds to the formation of bound dipoles (vortex-antivortex pairs) at low noise (corresponding to temperature in equilibrium). We show that - contrary to the equilibrium case - in driven-dissipative condensates these dipoles are always unstable towards unbinding, and hence such systems cannot support superfluid order.