I would call it a slight of hand trick. A hook on the end of the rod is suppose to grab the rubber band. The trick is to squeeze the rod between two fingers and snap it into the holder.
I made and sold similar 'toys' when I was in jr high and high school. I've had lots of fun with one of those. Hadn't seen one in 40 yrs. Thanks for the short walk down memory lane. I was really quite good at 'demonstrating' how it 'worked' and of course, no one else could make it work. Many would spend the longest time trying to make the 'hook' catch the 'rubber band'.
There are two ends of a rubber band protruding out from the sides. There is a hook on the removable "piston". You take the piston and "hook" the rubber band, which doesn't exist inside, and pull it back. Squeezing the top between your thumb and forfinger will make the piston shoot downwards making a snapping noise as it hits the outer tube. This gives the appearance of the rubber band "snapping" it downward. Then you hand it to your "pigeon" and tell them to try it. It's all in the "salesmanship" [][}]