  We consider the anisotropic gravity-gauge vector coupling in the
non-projectable Ho\v{r}ava-Lifshitz theory at the kinetic conformal point, in
the low energy regime. We show that the canonical formulation of the theory,
evaluated at its constraints, reduces to a canonical formulation solely in
terms of the physical degrees of freedom. The corresponding reduced Hamilton
defines the ADM energy of the system. We obtain its explicit expression and
discuss its relation to the ADM energy of the Einstein-Maxwell theory. We then
show that there exists, in this theory, a well--defined wave zone. In it, the
physical degrees of freedom {\i}.e., the transverse--traceless tensorial modes
associated to the gravitational sector and the transverse vectorial modes
associated to the gauge vector interaction satisfy independent linear wave
equations, without any coupling between them. The Newtonian part of the
anisotropic theory, very relevant near the sources, does not affect the free
propagation of the physical degrees of freedom in the wave zone. It turns out
that both excitations, the gravitational and the vectorial one, propagate with
the same speed $\sqrt{\beta}$, where $\beta$ is the coupling parameter of the
scalar curvature of the three dimensional leaves of the foliation defining the
Ho\v{r}ava--Lifshitz geometry.
