A two-dimensional and three-temperature mathematical model for dual-pulse laser ignition was applied to study the mechanism of the nonequilibrium plasma process during dual-pulse laser energy deposition. The two-dimensional model could predict the influence of the reaction kinetics and nonequilibrium effects on the ignition delay time and kernel dynamics. As the plasma reaction rates were extremely fast compared with the combustion reaction rates, it can be predicted that the variability of the plasma lifetime will directly influence the ignition delay time and reaction kinetics. The results suggested that the energy relaxation rate from the electronic state was rapid compared to that from the vibrational state due to the short lifetime of the plasma state. However, the relatively slower energy relaxation from the vibrational state provided long-term thermalization of the ignition kernel. For the same level of energy deposition, the nonequilibrium plasma system predicted a higher rate of vorticity generation, signifying a higher level of mixing and baroclinicity production. The results also suggested that ignition in a premixed fuel airflow required a higher degree of energy deposition, due to a higher rate of radical and thermal losses.