Dampner would be in the hub and not really contribute to that kind of slop. Seems more like a radial bearing is missing from inside the grip. Something letting the whole blade grip slide out too far. More than washers. That amount of movement looks more like a missing radial bearing. And it the missing part may be on the other "good" side. The dampers will be pretty tight on the feathering shaft so if you have that side drawn down tight and it is missing a piece or two, that can make the side with the apparent play look bad when in fact it is the other blade grip with the issue.
I'd suggest taking the blade grips off both sides, take the pieces out carefully (small pieces love to fall out and you don't even notice them or have a hard time finding them) and lay them out in the order and position that you remove them and take a pic so we can see what's there and what's not.
Should be something like:
screw, small washer, thrust bearing (three pieces), radial bearing, blade grip, spacer, radial bearing, washer, damper and then the same pieces in the opposite order for the other grip, in the middle the feathering shaft. You may only be able to get one of the retaining screws out. That's fine, do not try to grip the feathering shaft with pliers or something in order to get the other screw out. Just leave it in and note it. Don't want to mar the feathering shaft with plier marks, or worse bend it or deform it.