The answer to your title question is "moving air exerts a force on obstacles", and deep section front wheels are not special in being affected by that. Minimally spoked shallow section front wheels are also affected by crosswinds (but less than deep section because they have less facing area).

In any crosswind there will be some side force that applies a turning torque on the front wheel of almost any bike (viz, it is possible to design a bike such that this does not happen, but it may not be possible to ride the bike because the stability may be too low). The diagram below shows the normal design, somewhat exxaggerated as was the style in the 1960's:

[![enter image description here][1]][1]
(via the esteemed [Dave Moulton][2] whose post I got the image from contains an interesting discussion about why we have trail)

Note that the centre of drag/centre of the wheel is forward of the pivot axis. Thus, wind force from the side will tend to turn the wheel downwind, in the same direction that the wind is pushing the bike. So the rider will tend to stay upright, unless the turn makes them crash into something.

The bike you have pictured has the opposite design - as the wind pushes the bike and rider away, the drag behind the steering axis will turn the steering into the wind. I predict that in many cases the centre of mass will move downwind while the support moves upwind, resulting in a fall. But note that the front wheel design pictured is at best going to require clean, dry conditions to operate, and those are normally only found on indoor velodromes, making side winds a non-issue.

One interesting question is whether the neutral design with the centre of drag on the pivot axis would be more or less rideable than the picture you found, in any wind conditions.


  [1]: https://i.sstatic.net/YtVS1.jpg
  [2]: http://davesbikeblog.squarespace.com/blog/2007/5/4/trail-fork-rake-and-a-little-bit-of-history.html