By allowing Flora to escape, a horse due to be shot to provide meat for the foxes on the farm, the girl narrator lives up to the traditional expectations of society concerning how women are expected and taught to behave.
Up until then, the narrator went out of her way to behave like one of the boys, to help her father around the farm with the kind of tasks normally reserved for men. But for some reason—and even she doesn't know why—the narrator's softer, more "feminine" side, which she'd suppressed for so long, comes to the surface when she opens the gate to let Flora escape. Her prior curiosity over seeing a horse be killed has suddenly vanished. At the end of the story she is crying—behavior often expected of women—yet this action now dismisses her from working alongside the men, even though the girl does not feel fully on the "side" of the women in her family. Ultimately, her society punishes her, whether she is "one of the boys" or a traditional "lady."
As to whether the traditional differences or expectations between boys and girls outlined in the story are still relevant today, one would have to say no. It's fair to say that society in this day and age is more tolerant of men and women—though there is still progress to be made—going against traditional norms and even understanding that such norms can be harmful. Just as women can be hard-nosed, tough, and competitive, so too can men be sensitive, emotional, and sentimental.