In addition to "Bonedog", Charlie Kaufman also packs in a number of other references to a variety of art forms. Jessie Buckley's character recites large sections from Pauline Kael's review of A Woman Under the Influence, and there are also a number of references to Oklahoma! scattered throughout the film. All of these combine to make the viewer feel delirious and the effect may be off-putting to some people looking for something more conventional. 

I'm Thinking of Ending Things has already been interpreted in a number of ways, but one of the most common interpretations is that like the book it's based on, this story takes place inside the head of a lonely janitor who we see throughout the film. If that's the case, then "Bonedog" only reinforces that man's loneliness and his feelings of hopelessness as he goes about his life. 

Like the other references in the film, the poem is just something that the janitor read and enjoyed. It's trapped in his head, just like every other character in the film.