Whether it's because of similar desperation or not I don't know, haven't seen the show, but it's a very popular trend among TV show writers in Hollywood to use word plays like this in episode titles. Shows like Lost or The Wire made episode titling almost an art form.
By the way, the shooting horses bit refers to putting an animal (or person) out of its misery, the famous coup de grace (like when you kill a wounded soldier, one of your own or an adversary, who's in pain and won't make it anyway). According to wikipedia_
Distraught and despondent, Gloria confesses how empty inside she is. She tells Robert that she wants to kill herself, but when she takes out a gun and points it at herself, she cannot pull the trigger. Desperate, she asks Robert: "Help me." He obliges. Questioned by the police as to the motive for his action, Robert responds: "They shoot horses, don't they?".
The full story is about assisted suicide, as Gloria begs Robert to pull the trigger for her. The title and the final sentence point to this "coup de grāce", the "blow of mercy". For helping Gloria to commit suicide; the film shows directly, (and indirectly) that Robert will be found guilty of murder and executed by hanging. The marathon continues on with its few remaining couples, including James and Ruby. The eventual winners are never revealed.