Mine doesn't have the stoppers. I have a king size bed, too and it fits fine. It's a safety first (secure lock) from Big W that sits on top of the mattress. The part that goes underneath the mattress has "teeth" to stop it from sliding out from under the mattress. And it gets squeezed onto the mattress tightly so there is no chance of it moving. In my case it also is held in place by the side of the bed frame.
Babyzone Direct has it on their website, too for $50.9 on special at the moment (normal price $59.95) At least you can have a look at a picture of it there.
I hope that helps.
Sasa