In this type of story the major conflict is between giant, impersonal forces. They are the North and the South, the Union and the Confederacy. The protagonist is the Union, since they are on the offensive and are invading the South. Peyton Farquhar, like the anonymous Union soldiers, is only a little individual caught up in a gigantic conflict. He is helpless to do anything but wait to be hanged, just as the officers and soldiers are helpless to do anything except obey orders.
The company faced the bridge, staring stonily, motionless. The sentinels, facing the banks of the stream, might have been statues to adorn the bridge.
Looked at in this way, the conflict is largely physical--a military conflict between two armies. It can also be said to be moral, because each side feels it is in the right. And it can be considered emotional for the same reason.
The title of the story suggests that what is happening is just an unimportant incident, or "occurrence." The military forces involved in this region are small. The bridge spans a creek nobody every heard of. It is not even a river but a creek in the middle of nowhere. What happens is of importance only to one man who happened to be in the wrong place at the wrong time. In the few seconds of life he has left while falling from the bridge with a rope around his neck, he fantasizes about escaping and making it back to his home and his beloved wife. But his fate is inescapable, inevitable, and iinconsequential in the greater scheme of things. It is just a tiny incident in a great war that claimed over 600,000 lives.