From Wiki: The game is known as blind man's buff in the UK and Ireland, "buff" meaning a small push. It is possible that the American name is a corruption, or it may originate from the older sense of bluff meaning to blindfold.
Personally, I know it by this name, rather than the BEng. To me it makes sense because you can bluff by making a noise to draw the attention of the Blind Man and then move away as silently as possible. I do the same in Marco Polo.