What are the different parts of the plot in the story "the Coup de Grace" by Ambrose Bierce?

It's generally accepted that there are five core elements to the construction of any plot. These are:
1. The introduction, which sets up the context of the story, the key characters, and the setting, as well as gives some idea of what the later conflict will be. In this story, we learn that "the fighting had been hard and continuous" and that a burial squad is now taking care of all those who have been killed, laying them side by side in rows as graves are dug. An overview of the scene is presented, and then we meet "a man in the uniform of a Federal officer." This person is introduced to us not by name, but in terms of his state of mind, which is "not at rest." This gives us some hint as to what the conflict of the story will be.
2. The rising action. In this section, the key issue which will cause the major conflict in the plot is introduced: the characters we have already met will meet some challenge and begin to tackle it. This comes as we learn more about the unnamed officer: the man does not know where to go or what to do, and fears he "would hardly make a night of it alone among the dead." We see the man walk into the forest, making a decision which will cause the conflict of the story to arise. The man hears the occasional "low moan" from the dying, and then as he reaches a shallow ravine, stoops and lays his hand upon the face of one body, which screams.
This story is interesting in structure in that we now are presented with an interlude, a flashback of sorts which explains further who our officer, Captain Downing Madwell, is, and that there were two brothers, Caffal and Creede Halcrow, in his regiment. This section provides exposition of the type which might more usually be found earlier on in the construction of a plot: at the end of it we discover that Sergeant Halcrow has been mortally wounded in battle and Madwell has lost a third of his men.
3. The center or core of the story is the climax, also thought of as a point of no return. In the climactic sector, the protagonists must face their challenge head-on. In this story, there are two conflicts taking place chronologically in different places. The first is the conflict between Major Halcrow and Captain Madwell, in which Halcrow urges Madwell to push his company in a way which Madwell knows is futile—and which results in a huge loss of men. The second is the echoing conflict, a personal challenge to Madwell, of his encounter with the wounded man whom he discovers to be "his subordinate and friend."
We see that Sergeant Halcrow has been "mortally hurt." His small intestine is visible. He represents the visual aftermath of ruthless and unnecessary war. Because he is Halcrow's friend, Captain Madwell sees him through particularly pained eyes: he appears to him "the thing which had been his friend," having suffered "monstrous mutilations." Madwell, helpless, begins to cry; he cannot understand why this has happened and it seems very pointless to him. He shoots a horse between the eyes to put it out of its misery; Madwell ponders that he could not accord this same dignity to his friend, whose eyes yearned for death, because of some twisted sense of human morality. Finally, he goes back to his friend and attempts to shoot him, but it does not work—"he had used his last cartridge for the horse."
4. Falling action. This is what happens after the climax, and the effects it has upon the characters in the story and the steps they take to deal with its aftermath. In this story, the falling action is brief. Having finally screwed his courage to the sticking place, as it were, and attempted to shoot his poor dying friend, Madwell feels a sense of anti-climax. He does not know what to do now. Ultimately, he decides to take out his blade and kill his friend with his sword.
5. Denouement or resolution. This is the concluding section of a story, where the conflict is brought to an end and we learn what has been changed by the conflict. The resolution can be happy or sad. In this story, it is most definitely a tragic resolution. At the same moment that Madwell is plunging his sword into the sergeant's chest, three men appear, two of them hospital attendants. The third is the sergeant's brother, Major Creede Halcrow. The implication is that he, who has caused this pain in the first place and who does not know how Madwell has wrestled with himself, will now see Madwell attempting to kill his brother and judge him for it. The text silently asks the question: which of these two men is really the murderer?