Its true there is a fan in the base of all bladeless fans, but the fan is smaller then traditional fan designs and moves the same if not more air then traditional fans.
Air is pulled in through the base and forced through a thin slit. This fast stream of air creates an area of low pressure, drawing in and amplifying surrounding air behind the slits.
Because air "sticks" to itself, when you get some air moving (by breathing out, for example), the initial bit of air that you move "drags" some air with it from beside and behind. This is what Dyson calls "air multiplier technology".
Dyson uses this property of air to claim that they only have to move a fraction of air (with the fan in the base) of all the air that blows past you.
Here is a example of how this works, and how you can use one breath to fill a large bag.
Here is a image of the multiplier effect, from the original intake of air at the bottom. You can see the air is multiplied from behind and infront of the fan.
