A lot of the cables that I have used just have a plastic pin pushed into the hole. It looks like yours is this style. Take a straight pin and go at it from one of the corners and you should be able to dig the plastic out.
As others have mentioned, the old way to install the cable without the plastic cage around the pins is to find the #1 pin on the board, usually marked with a 1 or and arrow/filled in triangle pointing at pin #1. The number 1 pin on the cable is marked with a red line, squiggles, dots or some other way.
