Vidread,
The smallest island in the world - according to the Guiness Book of Records - is Bishop Rock.

In 1861, the British government set out the parameters for classifying an island. It was decided that if it was inhabited, the size was immaterial . However, if it was uninhabited, it had to be "the summer's pasturage of at least one sheep" - which is about two acres .
By this classification , I think the island you are referring to and many such islands around the world will not qualify to be the smallest island on the Earth