We present dynamical and structural scaling relations of quiescent galaxies at z = 2, including the dynamical-mass-size relation and the first constraints on the fundamental plane (FP). The backbone of the analysis is a new, very deep Very Large Telescope/X-shooter spectrum of a massive, compact, quiescent galaxy at z = 2.0389. We detect the continuum between 3700 and 22,000 angstrom and several strong absorption features (Balmer series, Ca H+K, G band) from which we derive a stellar velocity dispersion of 318 +/- 53 km s(-1). We perform detailed modeling of the continuum emission and line indices and derive strong simultaneous constraints on the age, metallicity, and stellar mass. The galaxy is a dusty (A(V) = 0.77(-0.32)(+0.36)) solar metallicity (log(Z/Z(circle dot)) = 0.02(-0.41)(+0.20)) post-starburst galaxy, with a mean-luminosity-weighted log(age/yr) of 8.9 +/- 0.1. The galaxy formed the majority of its stars at z > 3 and currently has little or no ongoing star formation. We compile a sample of three other z similar to 2 quiescent galaxies with measured velocity dispersions, two of which are also post-starburst like. Their dynamical-mass-size relation is offset significantly less than the stellar-mass-size relation from the local early-type relations, which we attribute to a lower central dark matter fraction. Recent cosmological merger simulations agree qualitatively with the data, but cannot fully account for the evolution in the dark matter fraction. The z similar to 2 FP requires additional evolution beyond passive stellar aging to be in agreement with the local FP. The structural evolution predicted by the cosmological simulations is insufficient, suggesting that additional, possibly non-homologous, structural evolution is needed.