High-order discontinuous Galerkin (DG) methods are attractive for simulating high-speed, high-enthalpy flows due to their accuracy and geometric flexibility. However, their application to non-equilibrium flows is challenging, as such flows involve strong shocks and steep gradients related to thermochemical non-equilibrium. Robustness and nonlinear stability are therefore critical. Entropy-stable (ES) DG formulations have proven effective for calorifically perfect compressible flows by enforcing a discrete entropy inequality, improving robustness without adding dissipation. This work extends ESDG formulations to chemically and thermally non-equilibrium flow models. We consider classical chemically non-equilibrium (CNEQ) formulations and, as an extension, two-temperature CNEQ (TCNEQ) models. Moreover, existing positivity-preserving strategies from the literature are incorporated into the DG framework to guarantee non-negative density, pressure, and thermodynamic variables, while minimizing the impact on high-order accuracy. The resulting entropy-stable and positivity-preserving formulation is assessed using benchmark cases, including the Daru-Tenaud test case extended to CNEQ conditions, and high-enthalpy flow simulations. Numerical results are compared with experimental data for hypersonic flow around cylinders and for supersonic flows around test samples in the inductively coupled plasma torch at VKI. Comparisons demonstrate the method’s ability to capture key flow features and non-equilibrium effects observed experimentally, while maintaining robustness and accuracy. Overall, the results indicate that the proposed framework provides a reliable basis for high-order simulations of non-equilibrium high-speed flows.