To me, the theme of this story is that it is best for people to be content with what they have and not to start dreaming of things that (they think) will be much better than what they have.
The couple in this story were relatively happy with one another. But then they thought they had won the lottery. Once they thought this, the husband especially began to have big dreams. He became dissatisfied with what a moment before had been an acceptable life.
Another way you could look at it is to say that the theme is that you should not let a change in your wealth (or other circumstances) change who you are as a person.