We employ first-principles DFT calculations to investigate the reaction mechanisms of Mg/CO2 chemistry on transition metal oxide (TMO) catalyst, RuO2 (Ruthenium oxide) serving as a cathode catalyst for Mg-CO2 batteries. RuO2 exists majorly in two stable phases such as rutile and anatase RuO2. The choice of rutile RuO2 is inspired by previous experimental and theoretical reports on their improved catalytic performance towards rechargeable Li-CO2 batteries, nitrogen reduction reaction, oxygen evolution/reduction, CO2 reduction, and hydrogen evolution reaction. To the best of our knowledge, there are no studies yet understanding the reaction mechanism and catalytic behavior of TMO, for example, rutile RuO2, for multivalent-CO2 batteries. XRD and HRTEM analysis of previous works report that (211) plane is one of the most commonly observed surfaces with the lowest surface formation energies, hence utilized to perform our computational investigations. We begin our study by evaluating the adsorption energies of the studied RuO2 (211) catalyst with reaction intermediates such as Mg, CO2, MgCO2, MgC2O4, MgO, and MgCO3. Next, we explore the optimal pathway for MgC2O4/MgCO3 nucleation and final discharge products in the Mg-CO2 reaction by analyzing the Gibbs free energies of different nucleation routes for MgC2O4/MgCO3. We found MgC2O4 to be a thermodynamically favorable discharge product on RuO2 (211) owing to their lower overpotential for nucleation compared to MgCO3 however, the energetically preferred MgCO3 nucleations on RuO2 (211) are observed as the final discharge products. We further elucidate the electrochemical free energies for the most favorable reaction pathway to investigate the role of the studied RuO2 catalyst in improving the electrochemical performance of non-aqueous Mg-CO2 batteries.