The damper tabs as supplied from Weber will not work on the WSM tabs without modification.
The vertical part of the damper handle has two small holes which firmly snap over the two dimples on the tab of a newer grill like a 18.5" or a 22.5". Older grills (like my old red MasterTouch) do not have the dimples, so the tab rattles around a bit. I've added the tabs on a couple of my other grills and they work fine, I guess I could take a punch and make my own dimples or just drill thru the tab & damper handle and insert a small nut and bolt. I just took a quick look last night, but the WSM tab looks shorter (and narrower)than a standard grill tab also it is bent at about a 45 angle vs the 90 on a grill.