DNNs are really well suited to unstructured data, which isn't the kind he highlights. One reason for that is because they automatically extract features from data using optimization algorithms like stochastic gradient descent with backpropagation. What that means is they bypass the arduous process of feature engineering. They help you get around that chokepoint, so that you can deal with unstructured blobs of pixels or blobs of text.
Because unstructured data is most of the data in the world, and because DNNs excel at modeling it, they have proven to be some of the most useful and accurate algorithms we have for many problems.
Here's an overview of DNNs that goes into a bit more depth: