Throws without touching are real, and have nothing to do with mystical powers property of aikido, or some mysterious force. It's just timming.
And I maybe most of us have done it at least once. For example, when we were kids, and you grab the ball for a friend who is going to kick it real hard, to score a goal. your friend runs towards the ball... kicks with all his might, but just before he actually hits the ball, you pull it, so he kicks air and lands on his back.
Well you throw him without toching him. Magic... NO...special power...NO, timing form your part, becasu if you take away the ball too soon your friend is going to stop, and if you take it away too late, then he's just going to kick the ball... and your hand probably.
So you have timing, and what happens with the kicker? well he was co confident taht he was going to kick the ball, that when it didn't happen, his mind was wondering "whta the hell happend? where's the ball?, whit his foot was still kicking. So descoordination between mind and body, and he falls.
Same in aikido
Aikido Goshin Dojo