Are you sure? (About the cross-section piece of your explanation...)
I read some time ago about how something like this worked in the laboratory.
When you play two frequencies together, you also produce the difference of those two frequencies, that is - so how it works is that they use ultrasound, say they play a 30,500HZ signal and a 30,000HZ signal - both of these tones are above the human range of hearing, but you will hear the difference - a 500HZ tone.
The added feature to the ultrasound method is that the audible tone(s) will not have a direction - like ultrasound, but will be easily audible - even though all tones transmitted physically are in the ultrasound spectrum and above the range of human hearing.
So they have built a simple speaker system to use this effect, and it's highly directional but requires only one transmitter, and not a 'cross-section' like stereo speakers would.
The advantage of having two beams that only intersect at one point is that the audible sound will appear to originate only from this one location. If the two beams run along the same path, there will will audible sound coming from all the points on this path. Of course the resulting sound will also be directional.
I have never seen either method in operation but I heard about the intersecting beam method from someone who should know (an expert on the physics of sound). Doing some research online though, I see that the systems currently marketed work as you say, with co-linear beams.
The Wikipedia article about this is here. (It seems to need a little more editing.) The most successful system being marketed appears to be the one called "Audio Spotlight".