Hitchens doesn't mean that empowerment of women is the only issue with regard to poverty, and he certainly isn't talking about "women's sufferage". What he is talking about is this:
In many places in the world where there is endemic and widespread poverty, women have essentially zero economic resources. Their only tasks are the raising of children and manual labour in either the home or fields.
One of the most effective ways that has been found for dealing with this poverty is the encouragement of small businesses. Often this has been done through Microfinance, and it's been widely noted that (for whatever reason) women have been the most effective recipients of Microfinance.
Here is a scholarly article looking at exactly this question.