...World" seems to be, "that stuff Columbus found (and never mind the Vikings)", the case could be made that Greenland is actually "Old" World.
OTOH, of course, they *did* have colonies in the "Real New World", as did Sweden. Both had some islands in the Carribean IIRC (Sweden's is (was?) called St Bartholome'), and what used to be New Sweden is now pretty much Delaware, I gather. Dunno if Denmark had anything on the North American mainland, though.