I have a friend who thinks the ropeless jump rope is a good idea. She reasons that normal jump ropes get tied up in your feet. That's part of the skill.
Without a rope, not only is there no motivation to jump, there's no reason to even have the handles to spin around either. Just jump without anything in your hands. No need to buy something for that.
But yeah, as far as the shake weight goes, people are so ignorant about exercise and nutrition that I've pretty much given up trying to explain it to them.
People feel the burning in specific muscles and they equate that with the fat burning away in that area.
If you want to lose arm fat, go on a diet and do some cardio. If you want to tone up your arms, lift some weights properly.
Normally if you shake something, you'd have to move your arms up and down, but this thing shifts its weight, so it becomes basically an isometric exercise. Exercises with no range of motion don't sound very efficient.