Clearly her previous iPhone experience was paramount.
But obviously, it wasn't like that when he first used it. It took time. For example, it took forever to teach him that if the hand that is holding it is touching the screen a little bit, then it won't properly register new touch events from the other hand. Eventually he just learned this, but it took a long time.
The other thing to note is that children actually learn how to use computers far more rapidly than you might think. It's not just devices like this, where people will assume that it is the multi-touch and intuitive interface that makes it easy for them to learn it. This helps, sure, but I was shocked when, after a mere two hours or so of usage, my two-year-old had learned how to navigate Flash games in a browser using the mouse. I was about to restart the game he was playing by clicking through the menus but no, he grabbed the mouse and did it himself, to my amazement.
Bottom-line: although I sense that many people will assume it is Apple's superior design that is responsible for this child's proficiency, I think that the combination of prior experience, plus the very quick learning abilities of young children, is a more important factor.