Their wires trail up through the ceiling of their home, presumably phasing through solid matter and into the sky. They're marionettes, so the only logical conclusion in this hallucination of a world is this: The wife and son's every action, and possibly every word they speak, is being controlled by an unseen god.
It's hard to tell how far this implication reaches beyond the walls of the family's home, but I've got some ideas:
1) The husband is being toyed with by a childish god. His life is like The Truman Show meets Team America. If this is the case, if this unseen god is messing with this guy for its own amusement, it's doing a s****y job of it. The husband seems happy. He cares for his puppet wife and son. When doubt of his love creeps in after he complains about the "ugly wires" of the receiver box, he quells their fears as a loving father would. When his human friend seems put off by his puppet wife, he defends her: