Bierce, or "the old gringo", has left America for Mexico in pursuit of life-affirming adventure.  He feels America has become corrupt, its people (himself included) cynical, and its idealism destroyed.  He sees Mexico and the Mexicans fighting as heros, passionate and honorable. 

Once amongst them, however, Bierce realizes his mistake.  They are also corrupt, full of skepticism and mistrust.  Tactics are dishonorable and behaviors controlled by emotion, as opposed to ideology.  It is Bierce's intentional miss during the execution of opposing soldiers that demonstrates how dissatisfied he is with the Mexican standards.