i suppose it might have been mistranslated, as meaning "since 800 years", as since 800 CE. that would rely on the norwegian claim. it's still not really right.
there was a political union in the late 14th century called the kalmar unon that included all of the norse speaking areas (sweden/norway/denmark/scania, plus colonies in finland and the baltics, iceland, parts of the uk, greenland and wherever else the norse had settled in north america, but not including normandy or england) and eventually, through many incarnations, became the rump state of denmark. denmark is a rump state that is directly descended from this union, while the other countries broke away to declare independence or got conquered by somebody else. however, europe had lost contact with greenland by this time, and we know today that they were no longer there.
it's not clear exactly what happened to the settlements, with theories ranging from being wiped out by a tsunami to escaping to canada to joining the inuit. there has yet to be any convincing evidence of norse settlement found in hudson's bay or the great lakes, but that does nonetheless seem to be the most likely theory.
the specific number of 800 years is just wrong. potential dates denmark could use are:
- erik the red, c. 1000 (founded norwegian settlements)
- kalmar union, c. 1400 (union of denmark and norway, but the settlements were gone)
- hans egede, 1721 (date of existing danish settlements)
none of them are 800 years.
i would suggest that the correct date is 300 years and that the danish colonization of greenland is not different than european colonization anywhere else in the western hemisphere and subsequently is subject to the monroe doctrine.