There is nothing particularly unusual about the structure of the story "The Cop and the Anthem." Indeed, its structure is fairly straight-forward. The tale is told in linear, chronological fashion; that is, events in the story happen in the order in which they actually happen to the character involved (no real flashbacks, just him remembering things on occasion.) It's fairly standard...if you look, you'll see that the name "Soapy" is within the first few words of each paragraph.
That said, it is also slightly episodic in that each of Soapy's encounters is kind of neatly contained as its own little event in the story. Little time is spent on the development of each of these into full-fledged elements and each exists only long enough to demonstrate how Soapy's goal of being arrested is thwarted.
It is a fairly strait-forward piece of writing, no less effective for it.