Pitcairn has a long established, permanent resident population so I would expect little impact to ham radio activities there.
Check out all of the entities that the group wants to put under a "No Take" status. Many more listed in the text of the article than even what are on that map.
I don't know exactly what the "No Take" phrase means, but this document seems to imply its mostly fishing:http://wiomsa.org/mpatoolkit/Themesheets/I1_No_take_areas.pdf
And I do understand the reason for trying to prevent over fishing . . . .