The Ender's Game quote you are referring to is spoken by Ender's somewhat frightening older brother, Peter. He says specifically,

Everyone thinks Hitler got to power because of his armies, because they were willing to kill, and that's partly true, because in the real world power is always build on the threat of death and dishonor. But mostly he got to power on words, on the right words at the right time.

Peter is a more complex character than he seems at first. He is essentially a violent personality, and yet as he grows up and takes on the alter-ego of Locke, Peter becomes something more. Through his essays, Locke (who is really Peter) manages to broker an international peace treaty. At the same time, Peter eventually becomes a powerful world leader known as "The Hegemon."

Although he no longer resorts to physical violence, as he did as a young boy, Peter works toward world domination. He accomplishes this through the power of his words. By uniting allies and wooing hesitant political groups, Peter gradually brings more of the world under his control. It is words, in the end, that condense his influence and make him into the last of the great world leaders.

You could also apply the power of words to the work done by Ender and his gentle sister, Valentine. They seek to tell the truth about what happened to the alien race Ender destroyed, and they accomplish that through research and writing. Valentine and Ender both become published authors, seeking to tell the Buggers' story from a different perspective. Although the deed has been done, it is only when Ender embraced the next step of hi destiny that he becomes Speaker For The Dead. Then, he is finally able to give voice to those who were lost.