Ah, yes, the floating disc. These sleds came with a floating disc...fixed calipers. Just the opposite of most cars and trucks with a fixed disc and floating calipers. Either design works.
Even when new, these sleds had a fair bit of wiggle to the disc.
There is a small, half-moon shaped key that fits in the jackshaft and engages a slot in the brake disc. It might be slightly worn. It a common as dirt size that any good hardware or automotive store would have, but you have to remove the jackshaft to replace it....kinda a hassle. And it's wonderful to put a dab of Never Seeze or grease on that key if you ever have it apart...that helps eliminate any rattling noise from the disc.
But, your probably fine.
You might check the brake adjustment. The nut at the top left of the chaincase at the pivot point of the brake lever adjusts the pad clearance. The service manual says to move the disc forward and backward and slowly tighten that nut until the pads just begin to move. That eliminates excess free play between the disc and pads. Obviously, don't tighten to the point where you have any drag on the disc.
The manual suggests replacing the pads if there is 7/16 inch of threads exposed after you have adjusted that nut. Don't worry too much if you do have that much. I've replaced the pads at that point before, and there is still a fair bit of pad material left.
The pads are a fairly quick, easy, cheap job to do when you need new ones.
So, you might check that pad adjustment, but don't worry about the disc....It's designed to float and center itself between the pads when you apply the brake. It flops around quite a bit when everything is in good shape.