My best guess is that it will dry out the surface of the dough. It may also pull some moisture from the inside of the dough, in addition to drying out the skin. A fan or breeze will let the air pull moisture from the dough - the exposure to a larger volume of air tends to pull moisture off, one reason it feels cooling. The effect should be greater as the recipe specifies cool air, which tends not to hold enough moisture or humidity to interfere with this drying.
It makes sense that a dough with a dryer skin may be easier to handle during the boiling step, being sturdier and less likely to stretch or deform while being handled. And I'm not sure, but I think a softer dough might be easier to work or shape, or the uneven drying to have other textural effects, which might be the reason drying the dough out a bit is better than simply using less water to begin with.
The dough will be boiled after this step, but while that will add moisture to the dough, the effects should persist. A dough that was dried before boiling will still have less moisture than a dough that was not, after both are boiled - boiling can only add so much moisture in such a brief time. Also, a dried skin on the dough would also help limit water absorption during the boiling, since the water has to work through the skin to reach the interior.
Time and temperature also make a difference - a soak would certainly soften the skin back up, but the recipe's brief dip in boiling water will not have time to soften the skin before the heat starts setting it. It would be similar to how starch forms sturdy, chewy lumps if dumped into hot water, but would dissolve in cold and when heated thicken the liquid smoothly instead of forming clumps. In this case, I'd guess the boiling would heat-set the starches of the dried skin faster than it can re-hydrate.
Another possible analogy that might help would be baking bread - the dough can easily form a skin when baking that changes the texture (by interfering with oven spring) which does not let it rise as easily, making a denser and chewier loaf. Since that texture is usually undesirable in bread, it is prevented by keeping the surface of the dough moist and pliable with water or oil, and scoring the bread to give room for expansion.
It is additionally possible that heat-setting the dough, by boiling, also helps to set the shape and support a sturdy skin on the dough in order to interfere with any oven spring the pretzel dough might undergo, again giving a denser and chewier texture. If so, both effects may stack for a more pronounced result.
Of course, much of this is speculation. The exposure to air will dry out the edges and form a skin, but it is possible that there are some additional benefits (controlling temperature or affecting starch structure, perhaps) that come from adding this step to the recipe that I am unaware of.