This is the usual definition, assuming NN, because it's a conveniently general model with a well-understood training method. However, to me, deep learning is a

This is the usual definition, assuming NN, because it's a conveniently general model with a well-understood training method. However, to me, deep learning is a more general concept: several layers to learn features, with a final classification or regression layer; where "layer" is some statistical learning process. The key idea is that features can be learned in a hierarchical way, not so much that they are NN layers, which is an implementation detail. For example, several layers of high-dimensional k-means unsupervised learning followed by a simple linear classification stage can perform very well.