Barriers don’t refer to how hard a discipline is skill-wise, they refer to how hard it is to enter the discipline. Law and medicine are also hard disciplines, but they have actual barriers to entry that cannot be surmounted by self-study. In this sense (which is the sense that the article means), programming does not have those barriers, no.

Considering that, unless you’re going to mount an argument that programming is objectively harder than those other fields skill-wise, it doesn’t seem productive to talk about an orthogonal “barrier” to entry that the other two also share. They are all difficult, so we end up in the same position.

Your comment here has spawned a large thread of people talking about how hard programming is (which frankly seems a bit self-congratulatory for this community, to be honest), but that’s completely separate from the core point being forwarded in the article; vis-a-vis, that programming is interesting and unique precisely because it has such a high compensation for a field without a central body limiting the supply (among other things). Law and medicine are also hard fields, and lawyers and doctors would be happy to explain why they’re difficult and have their own “skill-based” barriers aside from the licensing ones.