Beings of Tash Kalar
The pattern resembles a spiral. See? A spiral... Your eyes are getting heavy...
Yes, it allows you to move enemy pieces. And yes, it is a good idea to destroy pieces of the same color with these moves. It's hypnosis!
Well, it is completely up to you how you use the hypnotizing power: whether you will concentrate on destroying enemy pieces, on disrupting your opponent's progress toward the tasks, or on just making it harder to summon beings by moving the pieces away each from other.
The Hypnotist is one of the most controversial beings. I have often seen people who do not believe what they are reading ... so often that when I saw a new playtester heading my way with a puzzled look, holding an Empire card, I sometimes answered blindly even before he asked: "Yes, you can destroy enemy beings with these moves", and it was usually exactly what he wanted to ask about. :)
Actually, the problem is not the strength of the being, but its psychological effect. Destroying the pieces with your opponent's own pieces looks nastier than just destroying them, although in practice it is very similar.
Btw: Originally, Hypnotist had also an option to do 1 combat move with a legendary being. It was used so rarely that we decided to drop it to make the text on the card shorter. And in my very first game after the game was published, I badly needed it! :)