Mf12G Variable Speed Pulley

I have a little question.The variable speed pulley have a play from left to right . The pulley has to be tight to the axel ?
I have the impresion that something is missing.I have a little gap (space) between the pulley and the washer.Between theese should be some kind of bearings ? The washer has some grooves . Please take a look at the photos and give an opinion . When I screw the washer is not tight to the pulley .

Thank you .