Such a system, assuming it was feasible (which isn't) would not be practical, let me explain you why.
First, the principle behind it is to have the speaker and the listener being positioned at the focal points of an ellipse, similar to the whispering gallery.
The properties of the ellipse make it that the acoustic waves emitted in one focal point will converge into the other. But this mean that, once you have built your elliptical mirrors, you are bound to a fixed distance. Not one meter more, not one meter less.
But first you need to be able to build two elliptical surfaces with narrow enough tolerances that the waves are properly focused, which is rather challenging.
You can bypass the problem by building two parabolic surfaces (you just need to be able to spin a liquid fast enough while it becomes solid), but that would be less efficient, as you would lose part of your signal.
But at this point you would need an extremely precise alignment to be able to capture the acoustic waves. In practical this could be, at best, a though task, since you have to compensate for the motion of the air in between the two surfaces. Any shear in the wind flow will surely destroy the synchronization between the various paths, destroying the communication channel.
Late addendum: apparently the approach with parabolic surfaces was used in UK around 1920, to detect airplanes crossing the Channel. They could hear an airplane from 25 miles, giving 15 minutes of warning. More info here (page is in Italian). Mind that, being just a receiver, they were less annoyed by wind: they just needed the airplane to be at the suitable location.