Good spotting with Mexico - that's been added. French Polynesia is an overseas department of France, so is excluded. The others you name are all further away.
Yes, it's part of Chile, but note we exclude uninhabited islands. Easter Island is 6035 km / 3750 mi from the nearest inhabited island (Kiritimati). If we include uninhabited islands, it is 4680 km / 2908 mi from Caroline Island.