The poem reinforces the notion at the center of the movie that it's impossible to know another person the way you know yourself. As the movie suggests, it's impossible to know another person's thoughts, and so although you may think you know someone, you never really can. "Bonedog" is about that loneliness, and about how dreary it can be to live with the repetition of a normal life. 

Although there's plenty of beauty in I'm Thinking of Ending Things, the movie is also deliberately confusing. It's a puzzle where you feel like you must be missing a few pieces. In spite of the movie's general inscrutability, though, it's possible to grasp the ideas the movie plays with, including the loneliness described in "Bonedog."