"Physicists say they have made an object move just by watching it."
Physicists have a habit of describing what they have discovered in ways that interest the public, but are not really accurate--at least not accurate if you would ask the average guy.
If you've got a particle, you can't just "watch it." It's too small. You use a probe to see if it's there. Or you might shine a light on it, if it's big enough. You use high tech equipment to measure its charge, and that will give away its position.
Of course, when you do any of those things, the particle is nudged a little bit. When you touch it with a probe, shine light on it, or test its charge, it moves.
It would be more accurate to say that they are making it move by "touching it," but then that would not be such a big headline.