I'm afraid i'm not familiar with lga775 installation. I have one here on my desk which i was looking at, but i didn't realise you meant on the mounting mechanism. Both mine came with a different lga775 mounting mechanism to that.
Because the heatsink is symetrical i.e opposite sides are identical and so is the bracket in that picture there are only two ways round it can go.
On that pictured board the reason it must be mounted one way not the other is because the bracket itself interferes with the capacitors on the board. The actual heatsink is perfectly square so it won't matter which way that goes, its just the bracket that matters. Put the bracket on the board and see if interferes with anything on the board, if it doesn't then it doesn't matter which way it goes, if it does then turn it the other way.