Even Greenland usually counts as North America unless you explicitly exclude it, as the cited Wikipedia article does: "L'Anse aux Meadows is the only undisputed site of pre-Columbian trans-oceanic contact of Europeans with the Americas outside of Greenland."
The geology is just a happy accident of naming. Continents aren't defined by plates. Europe and Asia share a plate, except for a bit of western Siberia that's on the North American plate. The Americas have 3-7 different plates, but only 1-2 continents.
I'm in SE Canada a region called The Maritimes and supposedly there is evidence of Vikings visiting here. I'm West of Newfoundland but also an island. But Nova Scotia and even Maine in the US may have been visited by Vikings.
Technically Newfoundland is an island, but I would call that North America