From what I could tell from the lyrics, That Shakesperean Rag, although it references many of Shakespeare’s dark plays, seems very playful and light-hearted in a triumphant and glorifying way. The song is very “pop-py” and it’s no wonder that it was a popular song at the time.
In the poem though, the three lines from the hook of the song is interjected in the midst of the “conversation” that it going on between a shell shocked veteran and his wife. It is clearly ironic, how such a playful song is inserted into a scene that is all about the horrible aftermaths of the war and a love that is no longer. It is also telling that they mention lovers in the song, and how these lovers are nothing like Romeo and Juliet.