The answer to your question is not directly stated in Crane's short story of the untamed West, so the answer has to be inferred from the text and from the narrator's comments. Suspense and surprise are a large part of this short story. Note how we are not told until half-way through the story that Jack Potter is the Marshall and a fearless one at that?
[Said] the barkeeper, "He shot Wilson up once--in the leg--and he would sail in and pull out the kinks in this thing."
The information is delayed to build suspense and tension. We are told that Potter is important to Yellow Sky and that his marriage will have an important effect on the people of Yellow Sky but not why until the trouble with Wilson has begun. This delay of information is to build suspense and tension, and it succeeds. We keep asking, "Who is this guy? Why is he important?" We keep feeling, too, that maybe we missed something and reread a time or two!
As a result of Crane's choice to delay and withhold information we have to use what we are told about the relationship between Potter and Wilson and about Potter's role in the town to understand Wilson's surprise reaction at the end of the story. We also have to apply the narrator's mysterious (to readers of today, perhaps not to Crane's original readers) statement: "in the presence of this foreign condition he was a simple child of the earlier plains."
So, what can we infer from these two sources of textual evidence? We can infer that Wilson and Potter have an antagonistic relationship when Wilson is drunk. We can infer that Potter's aim is to keep the peace and to stop Wilson's terrorization by whatever means is needed (note that he shot to stop Wilson, not to seriously injure or kill him: he shot him in the leg). We can infer that Wilson is looking for a fight from Potter:
But still there was no offer of fight. The name of Jack Potter, his ancient antagonist, entered his mind, and he concluded that it would be a glad thing if he should go to Potter's house and by bombardment induce him to come out and fight.
We can infer that there was an ancient law of the land, of "the earlier plains," that dictated that a newly married man was not fair game for a gunfight: "Historically there was supposed to be something infinitely humorous in their situation [of being newly married]." While the text admits to humorousness attached to the newly wedded estate (a humorousness that is lost in today's social climate), the text suggest that there is also a special form of respect and peacefulness attached to it as well.
So why did Wilson walk away and did he walk away in disgust? There is nothing in Wilson's deportment or his scattered words to suggest disgust as his reaction. In fact, his reaction is one of wonder and amazement:
He was like a creature allowed a glimpse of another world. He moved a pace backward, and his arm with the revolver dropped to his side. "Is this the lady?" he asked.
With this understanding and with an understanding of the special status awarded a newly wed couple, we can conclude that Wilson walked off because he is amazed and prevented from further antagonism by the social laws "of the earlier plains" days. He simply knows there can be no fight today and no fight with Potter today because today is a day to acknowledge newly wedded bliss and peace. He leaves in wonder and because the fight is all gone from within him; he does not leave in disgust, which would provoke further fight.
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