Air surrounding the edges of the fan will also begin to flow in the direction of the breeze. This process is called entrainment. Through inducement and entrainment, Dyson claims its fans increase the output of airflow by 15 times the amount it takes in through the pedestal's motor.
Advertising for a product isn’t a citation. That article literally just repeats Dyson’s own claims. Do you have anything that actually tests that claim?
I don't think you two are even contradicting each other. The airflow going through the base can be 15x smaller than the total result, but also require more energy than just using a regular fan that moves that amount of air.
Total airflow and efficiency are two independent things.
Disclaimer: I have no real data on how Dyson fans work.
As demonstraded by the ActionLab video someone else posted, "bladeless" fans in general are less efficient. The one he tested was not a Dyson and didn't have a HEPA filter.
You made an assertion. If you are unable to provide supporting evidence, we can assume that your assertion is incorrect without needing to prove anything.
They're "bladeless" fans are just regular fans with more steps. Those added steps introduce inefficiencies. Simple as that. If you wanted to make a fan more efficient, you could add a shroud close to the blades, but the energy cost of electric fans are already low enough that it really doesn't matter.