Gaseous detonation is regarded as a promising combustion mode in novel detonation engines. The numerical simulations with high fidelity of the gaseous detonation require the detailed chemical mechanism and the high numerical scheme resolutions, and therefore lead to the expensive computational costs. In the present work, a parallel algorithm based on the storage/deletion method is selected to accelerate the chemistry computations in the numerical simulations of two-dimensional gaseous detonation wave propagation. The effects of fuel type (chemical reaction mechanism) and numerical scheme resolution on the acceleration performance of the selected parallel algorithm are studied. Two gaseous fuels, hydrogen with smaller chemical reaction mechanism size and ethylene with larger one, are chosen to carry out the simulations; while for the numerical scheme, the weighted essentially non-oscillatory (WENO) scheme with fifth-order and ninth-order resolutions are respectively employed. It was found that the parallel algorithm can provide the satisfactory performances on both computational accuracy and efficiency for all simulations in present study. The fuel type (chemical reaction mechanism) has a more obvious influence on the computational efficiency, while the numerical scheme resolution has a relatively unimportant effect during the entire simulations. The hydrogen chemistry has higher speedup ratio than the ethylene chemistry at the early stage of simulations, but the speedup ratios of both fuels will finally converge to the similar level at the later stage. The optimal speedup ratio of 4.67 is obtained for the case with the ethylene reaction mechanism (larger size) and the ninth-order WENO scheme (higher resolution) at the end of computations. Furthermore, the balance and synchronization of table operations among different data tables in the parallel algorithm are analyzed. Neither balance nor synchronization can solely affect the acceleration performance, both of them jointly play the important roles in accelerating the simulations of gaseous detonation.