It is an interesting article but raises some questions about the use of the word protein function.
Some 40 – 50 years ago, enzyme protein activity were considered somehow apart from protein function. The first word (activity) was used for the biochemical definition and resulted in a complex number of a catalog that was usually linked to the chemical reaction whose velocity was increased by the catalytic action of the enzyme.

Enzyme function on the other hand, was strongly influenced by the research made in microorganisms that indicated the effect of nutritional factors upon gene expression control. Operon lac was the best example.

Whenever a reference of protein function was made about proteins of more complex organisms a great care was taken in order to clearly indicate organ, tissue and condition of study.

I am not by any means, describing microorganisms as simple ones, I have worked with some very interesting ones and always followed the line of reasoning presented by Davis, Dulbecco, Eisen, Ginsberg and Wood in Microbiology 1970 where they say in a more or less strict text form something like this: “... those that consider microorganisms simple forms of life have never worked with them.”

Therefore, to me, whenever you refer to amino acids of the activity site you are much closer to a relation to enzyme activity than to enzyme function.