It probably works like an ejector pump. Deep well jet pumps use this principle. A high speed jet of fluid (air, water) will accelerate the fluid around it thereby moving a larger quantity at a lower velocity.
Dyson uses a ring shaped jet to “pull” more air through and around the ring. Neat execution.
If you have access to a garden hose try this experiment. Run enough water on the pavement to make a puddle. Try for 6 feet diameter or larger and at least 1/2” deep. Set the hose nozzle on a high speed jet position, hold it close to horizontal and aim the stream at a point about 1/3 of the distance across the puddle. The stream will hit the puddle and continue, pulling additional puddle water with it and eventually emptying the puddle.
Voila! an ejector pump.
I’ve got a birdbath that I clean by directing a stream of water at the inside edge. Amazes me that it spins all the water out within seconds, taking all the leaves and crud with it, resulting in an empty bowl. Similar idea to what you’re saying in your experiment.