That's an interesting question.

On the surface of a liquid or in the volume of a gas, a disturbance impacts every adjacent point, in every direction. A little pressure wave goes out in every direction from the point of disturbance. On the 2-D surface of a liquid like a pond, you get an ever expanding circle. In a 3-D volume like a gas you get an ever expanding sphere.

There are ways to guide or focus this energy initially, but as soon as the little pressure wave is in free space, away from the thing that disturbed it, it starts behaving this way (in every direction.) Even things as tightly focused as lasers diffuse as they pass through gas and liquids, for the same reasons sound does.

Now think of your string not as one thing but as a collection of an infinite number of points (which it is). As it moves, it's disturbing the air around it at every single one of those points, initiating an ever expanding sphere from each. The disturbance does not just travel perpendicular to the string. It goes out in all directions from everywhere on the string. Again, this can be directed initially like we do with speakers and guitar bodies, but as soon as the wave is away from the surface of the speaker or out of the guitar, it starts going in every direction.

Hope this helps. Again, thoughtful question.