But why?? We have had rocket powered anti-aircraft interceptor drones that go at mach 3 since 1955.
Anyone can build this style of interceptor with commercial off the shelf parts for a a few thousand dollars. It's also reusable. A rocket for the same budget will be unguided and single use. Not useable as an interceptor.
Maneuverability and cost. Why this specific stunt? Marketing, presumably.
Cost, your average stinger cost 38000 dollars in the 80s. I am guessing here but they are aiming at a price of probably under 10000 dollars.
Now why doesn't anyone take a rocket and stick the drone guidance on it? Again I am only guessing here, the drone guidance components probably can't cope with 2-3 mach. At 1000 meters per second with a 60 fps camera you advance 16.6 meters per frame, add to that the latency of whatever guidance system you have. You are looking at 20-30 meters offset between frames.
Better guidance probably balloons the cost to the 10s of thousands of dollars.