The conflict of individual vs. technology affects the story because there are no characters except the non-living house and robots.
The story involves a post-apocalyptic society where all of the living things have been killed by some disaster. The only thing actually alive is a dog in very bad shape.
The morning house lay empty. The clock ticked on, repeating and repeating its sounds into the emptiness.
The apocalypse was likely caused by some kind of atomic explosion. Little if no life forms survived. The explosion was likely recent, because the dog is still alive and the house is still well-stocked.
This conflict affected the plot because without the bomb, the people would not have been killed. Because the people were killed, the house destroyed itself. The fire was caused by lack of human contact, and the house could not put it out.