Sorry, I do not believe what the web site is saying.
Here is an experiment Sherman can do and help us understand the question:
Place the candle further and further away from the hair blower and see the effect. (Test the air pressure. The further the wind source, the smaller the low pressure.)
Use this distance, change the temerature of the wind blowing, perhaps by using the fridge and heating element of the dair dryer. (Test for temperature. Is it true that people in Arctic has an easier time blowing out candle than say, African?)
Lastly, to proof what the web site is correct, it should be impossible to blow out a lighter because you can't "blow off" the flame. So change the fire source and try it again to see if there is any difference!
Are you sure the electric heating element of the hair dryer will "burn" any oxygen away? How about a safer way with air from freezer, or air from top of a block of ice? If temperature is an issue, cooler air should be able to do it better, right?
Actually I found an even more likely answer, it fits with all observations I seen so far in my life:
I think the wind blow the chain reaction of the fire away. In order for the flame to continue, the last reaction must be in proximity with the next reaction in order to transfer the heat.
With the air moving so fast, it outpace the reaction front.
This is observable as the wind gets stronger and stronger, the flame moves away from the head. At certain wind speed, the flame will bound to be too far from the fuel source.
** I think the temperature idea is correct only concerning candle because of the way the fuel is supplied (vapourization of the wax). It is incorrect in the general sense.