A bout is related to about which comes from the sense of a roundabout. The circularity is in all of them. A bout is also called a round. I think this is to do with it completing a circuit in each section.
About isn’t always round – sometimes if someone is, say, skipping about, they’re traveling all over the place, not necessarily a circle.
And when we ask what a story is about, we’re not necessarily thinking of a summary as a circle. There is a great deal more circularity under our language than I realized.
The Hamlet Project 