how does the phrase nothing personal contribute to an understanding of the events in the story?

The last line in the story is spoken by a less than empathetic truck driver:

I'm sorry. I can't help it, Mr. Thomas. There's nothing personal, but you got to admit it's funny.

Mr. Thomas is visibly distraught over the destruction of his property, yet all the truck driver can do is laugh. It would appear that he, like so many in this war-ravaged society, has become immune to destruction, so much so that all he can do is laugh in the face of it. Like the boys who wrecked Mr. Thomas's property, the truck driver is working-class, and there's an element of inverted snobbery about his callous disregard for someone else's property. It's unlikely that he has any property of his own and so finds it hard to empathize with the loss of someone else's.
In political terms, one can see the truck driver's tactless remarks as indicative of a more collectivist spirit in British society. This is the era of the Common Man, in which the hierarchical society of pre-war Britain is being changed from top to bottom by a radical Socialist government. The truck driver likens Mr. Thomas's house to a man in a top hat. And just as a man in a top hat is out of place in this bright new Socialist utopia, so too is Mr. Thomas's house amid the charred, rubble-strewn landscape of this down-at-heel neighborhood.