But then you (and the author?) talk about different things than the Wikipedia entry that the author linked to, because that entry (and what I remember about structured programming--but I was very young, so might have missed a lot) specifically talks about "making extensive use of the structured control flow constructs [...], block structures, and subroutines", also mentioning Dijkstra's "Go To Statement Considered Harmful" and some debate around that.
The structured program theorem is also about specific control structures, essentially proving that they are Turing complete by themselves. I remember that we had to prove in university that as a result, you can transform any program into a program with one big while loop. (I think that's equivalent to "μ-recursion", whereas the simpler "LOOP" statement only implements "primitive recursion" which is not Turing complete, but it's been a while.)
What you talk about sounds like it could be "modular programming", of which Wikipedia states: "Modular programming per se, with a goal of modularity, developed in the late 1960s and 1970s, as a larger-scale analog of the concept of structured programming (1960s)."
Of course, Wikipedia is not a good source, I wasn't there when it started, and it's entirely possible that structured programming meant more back then than it seems to mean today, or meant different things in different circles. A quick Google search seems to confirm that nowadays structured programming primarily seems to be the use of control structures, though maybe that's just what survived?