This study investigates the performance of Genetic Algorithm for optimizing binary neural network controllers in the Atari Space Invaders task, extending prior work that applied Evolution Strategy to the same optimization problem. The network topology and the activation function are kept consistent with the earlier study to enable direct comparison between GA and ES. Two GA configurations were utilized while varying the number of hidden units and the bit precision of connection weights. Experimental results revealed that, for the number of hidden units of 1, 2, 4, and 8, the game scores achieved by 1-bit networks were not significantly lower than those of 64-bit networks, consistent with prior ES-based findings. Moreover, even a single hidden unit exhibited competitive performance, unlike in the ES case where performance degraded markedly. GA outperformed ES under the configuration emphasizing the number of generations, while ES performed better under the configuration emphasizing population size; the former difference was statistically significant (p < .01). These findings suggest that GA provides a viable alternative to ES for training binary neural network controllers in reinforcement learning tasks.