The absence of female soldiers in this story does suggest a double standard. It is clear that in this culture, men are supposed to fight wars. The absence of women suggests that the culture might deem women to be too weak to be soldiers. Other than the old woman who points out the sniper's position, there is not another reference to a female character. This further underscores the point that not only is war not a place for women, but also it is not a place for men to even be thinking of women.
The philosophical focus of the story is more broadly on the inhumanity of war. It is an illustration of how cold and unsympathetic a soldier must be in order to become used to killing and violence. The sniper, our protagonist, is so robotic that he has no problem killing the old woman who informs on him. Given the more broad philosophical statement about the inhumanity of war, it doesn't seem that this is also a comment on women being expendable. However, using a feminist lens, the woman's death might suggest a subtext that is obscured by the more general statement about inhumanity.
In the sniper's defense, he is simply reacting in self-defense. And after shooting her, he doesn't have time to reflect upon what he's done because he is immediately under attack by the enemy sniper. From the reader's perspective, using a Feminist lens, she is collateral damage. The sniper would have shot an old man just as easily, so there isn't an overt statement on gender issues in this killing. Just to delve a bit deeper, note that the woman functions as a subordinate. She has no real position of power. The men have the weapons and make the decisions. She is a pawn in their dangerous game. She is just as vulnerable in her position as an informant as the soldiers are. But since she has no power and no ability to defend herself (being armed as a soldier), she is at a disadvantage. Even if this were a younger woman, the statement would be the same. She has less power and less means of defending herself, but her culture has encouraged her to put herself at risk anyway. This could be read as a particular event that illustrates the plight of women in a more general way. Less power and less opportunity leads to a life with less advantages. Thus, the double standard manifests in many different ways.