Micro-Missiles

 

In all likelihood, Baggett didn't really "shoot down the plane", instead, he presumably shot and killed the pilot with his pistol causing it to crash.

Killing or disabling the operator (either human or AI) of an aircraft, or ship, or tank, or missile battery, or other vehicle or military system requires profoundly less explosive force and a profoundly smaller projectile than using a projectile transmitting explosive force to render the equipment being operated inoperable.

There are a couple of fictional examples of the idea.

One is in the anime Gargantia on the Verdurous Planet (2013) in which a mecha fires tiny guided missiles to kill or tranquilize (I don't recall) the members of the enemy crew on a warship bent on destroying the peaceful flotilla of our hero's friends.

Another is Frank Herbert's Dune series (the first volume, was published in 1965 and contained the point key to this post) in which war between massed armies has been largely abandoned because shields are effective against most projectiles, and atomic weapons sufficient to overcome shields are too destructive to be used without destroying what one wants to conquer. Instead, war is waged primarily via bird sized assassination drones targeted at enemy leaders and other key personnel. 

At the time Dune was written, the technology to do this was hopelessly out of reach. In 2013, it was imaginable, but still an extreme concept. In 2021, we are approaching an area, however, where this kind of tactic might be viable.