I would agree with you if the author did not explicitly say what he meant, and assumed the reader knew what he meant, but the author did not make any such assumption.
In order to quell the issue of "functional" having many definitions, the author chose one, and wrote about it. I don't see your alternative, which seems to be "accept that functional means something different and write about that", as one that is worthwhile to pursue.
Maybe to acknowledge that "functional" is used with a different meaning, often, would be sensible rather than just pretending all one needs to do is re-define it from common usage and proceed.
People are not compilers. If you want to redefine a word that is already in your readers' vocabulary with a meaning ascribed you've kind of got to talk about why you're doing that and why your redefinition is worthwhile and the alternative, generally accepted meaning needs to be jettisoned. Or you risk unintentional impersonation of a crank, which would be a shame if you're actually correct.
The point here is that the definition in the article is not something new. The author merely chooses to pick an accepted definition of functions, and build from there.
You makd it look like he's trying to push a new definition, which is not true.
In order to quell the issue of "functional" having many definitions, the author chose one, and wrote about it. I don't see your alternative, which seems to be "accept that functional means something different and write about that", as one that is worthwhile to pursue.