Harrison's parents are not emotionally affected much at all by the death of their son because they cannot be.  

For Harrison's mother, Hazel, her "perfectly average" intelligence does not allow her to become emotionally invested in much of anything. Even when she speaks to her husband in a caring manner about his health, it is quite shallow. She calls George "honeybunch," but the word feels void of emotion. Hazel's intelligence only allows the most basic of human responses. Even when the story reveals that Hazel has cried after viewing the death of her son, Vonnegut makes it clear that she cannot sustain thought or emotion by including this exchange between George and Hazel:

"You been crying?" he said to Hazel.
"Yup," she said.
"What about?" he said.
"I forget," she said. "Something real sad on television."  

Harrison's father, George, could be emotionally affected by the death of his son if he did not have to wear the government-issued handicaps that keep him from feeling deeper emotions and thinking deeper thoughts. Because he has been handicapped due to the government's desire to make society completely equal, he cannot muster up any thoughts or emotional reactions that would be better than the lowest common denominator's thoughts and emotions. When George starts to think and feel, incredibly distracting sounds stop his flow of thoughts. It's not that he does not want to feel emotional about his son's death, he just can't.

Why don't Harrison's parents react emotionally to what they've witnessed?

In the dystopian society depicted in such horrifying detail by Vonnegut, people aren't supposed to feel anything. They're simply supposed to do what the government tells them. For its citizens to enjoy a rich emotional life is dangerous to the government, as it provides a haven of repose, a personal space where people can escape the state's control. Handicaps must then be used to enforce not only a crude physical and intellectual equality but also an emotional one. So when the Bergerons watch their son's death on live TV, they've been so emotionally crippled that they're unable to feel sad for more than a few brief moments. Hazel is not a particularly bright individual, so she's naturally handicapped and inured to any deep emotions. George is naturally intelligent, however, and so he is forced to wear a radio device that emits loud noise at regular intervals to prevent him from experiencing sustained thought or emotion.

Harrison's parents do not respond to what they see on the television screen because Hazel is rather dull and George must wear a handicap on his head that prevents his thoughts from forming.

Whenever George has a thought that is the least bit complicated a buzzer goes off in his head, destroying his ideas and injecting pain. Hazel is naturally "normal," so she is not intelligent and sensitive enough to experience anything but the simplest feelings. When they see their son Harrison on the television screen after having heard that he has escaped from jail, they do not react in the expected manner of parents because George has a terrible ringing from his handicaps, This ringing in his ears prevents George's thoughts from forming as they normally would, while Mable is simply not capable of feeling anything of any depth.