  We investigate the out-of-equilibrium behavior of a dissipative gas of
Rydberg atoms that features a dynamical transition between two stationary
states characterized by different excitation densities. We determine the
structure and properties of the phase diagram and identify the universality
class of the transition, both for the statics and the dynamics. We show that
the proper dynamical order parameter is in fact not the excitation density and
find evidence that the dynamical transition is in the "model A" universality
class, i.e. it features a non-trivial $\mathbb{Z}_2$ symmetry and a dynamics
with non-conserved order parameter. This sheds light on some relevant and
observable aspects of dynamical transitions in Rydberg gases. In particular, it
permits a quantitative understanding of a recent experiment [C. Carr et al.,
Phys. Rev. Lett. 111, 113901 (2013)] which observed bistable behaviour as well
as power-law scaling of the relaxation time. The latter emerges not due to
critical slowing down in the vicinity of a second order transition, but from
the non-equilibrium dynamics near a so-called spinodal line.
