"The man who was engaged in being hanged..."See in text(I)
This is an example of Ambrose Bierce's cynical humor. By using the present participle, Bierce makes it seem as though the condemned man is willingly helping the soldiers to hang him. Bierce was known for his cynicism, and it is common within Bierce's work.
The water is moving swiftly but the condemned man sees it as moving slowly, indicated below where he thinks, "What a sluggish stream!" The narrator specifies here that the water is moving swiftly because it will be important later in the story.
