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 suffrage". 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. For these and other reasons women are hugely more likely to be poor than men.
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. Again for whatever reason, these businesses also appear to raise the economic level of the community they live in.
Here is a scholarly article looking at exactly this question. Here are some others: