To be clear, there are neural networks which are "deep", and others which are "shallow" (few hidden layers). From a practical standpoint, the latter have more in common with other "shallow" learning methods (tree-induction, statistical regressions, k-nearest neighbor, etc.) than they do with deep learning.

You're right that many people (especially in the non-technical press) have erroneously used "machine learning" to mean specifically "deep learning", just as they've used "artificial intelligence" to mean "machine learning". Regardless, there are still non-deep machine learning methods and other branches of A.I. In practice, non-deep machine learning represents the overwhelming majority of applications today.

I haven't followed the research as closely in recent years, but I can tell you that, deep learning aside, people have only begun to scratch the surface of machine learning application.