This story addresses the very common question of why people treat others cruelly for no reason. In this case, the answer is both pyschologically and socially complex.
First of all, the Wosley Common Gang, a group of young teenagers, is seeking to emulate the older, tougher gangs of the time. In an effort to be like their idols, the boys seek trouble. Their choice is a defenseless man who is going to be away from his house for two days. Thus, their "trouble" is going to be easy. Thus the boys are moving from the innocence of their youth into the darker days of adulthood.
Another reason is the shift of control from Blackie to Trevor. Both boys feel the need to assert authority, and the escalation of the destruction to include the burning of the money shows this need to impress.
The social and psychological situations lead the boys to the utter destruction they impose, though no clear cut reason for the specific target exists. They probably could not give you an answer themselves.