AI is the overall field and the superset of all of the various approaches.

ML is one family of approaches for knowledge acquisition in AI, but far from the only one (eg. logic based inference is another big one).

DL is a family of approaches in supervised ML. As the author points out, it's a subset of a subset.

But saying that this sub-subset "drives" AI is like saying endocrinology "drives" medicine: not the right mental model at all.