The zero-temperature critical state of the two-dimensional gauge glass model is investigated. It is found that low-energy vortex configurations afford a simple description in terms of gapless, weakly interacting vortex-antivortex pair excitations. A linear dielectric screening calculation is presented in a renormalization group setting that yields a power law decay of spin-wave stiffness with distance. These properties are in agreement with low-temperature specific heat and spin-glass susceptibility data obtained in largescale multicanonical Monte Carlo simulations.