I think that southern Paeonia to north of ancient Macedonia was annexed by Phillip II and it is in today's slavic Macedonia. Map you posted is a nucleus of Macedonia before Phillip''s and Alexander's conquests in all directions. They also did some northern and western land acquisitions although they were not far reaching. They preferred peaceful border with Illyrians.
The Slavs of the region of Macedonia are very much attached to the 19th century concept of Macedonia, which is based on a map of a German historian. Their self-identification has been greatly influenced by this geographical connotation.
The name Macedonia survived because of the Greek literary tradition which has a continuous documentation since antiquity. It is the only language which has been spoken continuously since antiquity in the region of Macedonia. Without it, the term Macedonia would probably not have survived in the first place.
There is reason enough for the Greeks to feel robbed of their heritage. But the Macedonian Slavs didn't use that name over night either (although they received a great boost during Tito's reign). Let's hope that this treaty will do more good than bad.