What are the advantages of this gold finger shape?
To electroplate the fingers with gold they must all be joined together electrically. This is done with a "plating bar" trace outside the final board area, which is cut off afterwards. 



Usually the board edge will be chamfered for easier insertion in the socket. Since chamfering removes the lower part of the fingers they only have to be wide enough to carry the electroplating current. Making them narrower saves gold, which makes the board cheaper. If the board is not intended to be plugged in often then chamfering may not be applied, and then the narrow parts remain.

Gold plating for edge connectors