  We develop a transfer operator approach for the calculation of R\'enyi
entanglement entropies in arbitrary (i.e. Abelian and non-Abelian) pure lattice
gauge theory projected entangled pair states in 2+1 dimensions. It is
explicitly shown how the long-range behavior of these quantities gives rise to
an entanglement area law in both the thermodynamic limit and in the continuum.
We numerically demonstrate the applicability of our method to the $Z_2$ lattice
gauge theory and relate some entanglement properties to the
confinement-deconfinement transition therein. We provide evidence that R\'enyi
entanglement entropies in certain cases do not provide a complete probe of
(de)confinement properties compared to Wilson loop expectation values as other
genuine (nonlocal) observables.
