The house symbolizes the destructiveness of technology because the humans are all dead and the house continues on.
It is clear that whatever happened to the people was some kind of technological disaster. Nothing in nature turns a family into spots of paint. The entire wall of the house is blackened, everything living is dead, and the dog crawls to its death. There was likely some kind of nuclear blast that destroyed the population.
The five spots of paint—the man, the woman, the children, the ball—remained. The rest was a thin charcoaled layer.
The house itself continues to be alive, because it only mimics life. It is not susceptible to the radiation. The house survives and goes about its business without realizing that the people are not there. It has no appreciation for life, as evidenced by its cleaning up the dog's body like so much garbage.
Two o'clock, sang a voice. Delicately sensing decay at last, the regiments of mice hummed out as softly as blown grey leaves in an electrical wind. Two-fifteen. The dog was gone.
The dog is swept up and incinerated, and that is that. The house cannot distinguish between it and the garbage. It was the only living thing that remained, but it meant nothing to the house.
The house would have continued indefinitely if it had not been destroyed by the fire. The fire was an accident. A tree branch knocked over a can of solvent. If a person had been there, he or she would have realized what was going on and put out the fire before it burned down the house. The house itself was incapable of logic. It tried to put out the fire and failed.
Ironically, the tree's death is undoubtedly linked to the atomic incident that incinerated the family. The house died for the same reason the people and the dog did, at least indirectly. Technology killed the house too.
Bradbury is trying to tell us with this story that while it may be nice to have technology help us, it can hurt us too. If you allow everything to be automated and rely on machines to help you live your life, you run the risk of being disconnected from what really is life. Something happened to the living in this story. We do not know exactly what, but we do know that technology is to blame.