It is called an LPH - Landing Platform Helicopter. A Destroyer is long & narrow and much smaller.
(idiot AP writers)
IIRC, China just launched an LPH, but I cannot find the story.
I believe that Japan is referring to it as a 'destroyer' for the same reason that the Soviet Union used to refer to its aircraft carriers as 'cruisers'. Japanese law prohibits the building of carriers or other offensive weapons, just like treaty prevented aircraft carriers or other capital ships from passing through the Dardanelles without Turkish permission. So it's subterfuge in both cases.