"Harrison Bergeron" is written from third-person perspective, although there are insights into George's thoughts included in the commentary. The story presents itself as being a fairly factual and straightforward report of the dialogue between George and Hazel while they were watching television and the events that they witnessed.
However, the sarcasm and black humor contained in the commentary sets the tone for the story. This is not what any contemporary reader of the story would interpret as a normal couple spending a quiet evening relaxing at home. This is a man being tortured by devices that have been inflicted on him by the government, and they are watching others on the television who are also being severely penalized for aspects of their physical and/or mental beings that they have through no fault of their own.
Vonnegut is pointing out the absurdity of a society attempting to create artificial conditions that make all people equal by presenting his vision of what such a society might look like. He is also issuing veiled comments about the dangers of a government that has too much power to interfere with too many personal aspects of the every day lives of citizens. While presented in seemingly innocent terms, there is real frustration and concern for the future under the surface of this story.