Who gets the point in this hypothetical badminton move?

What you describe is just a fancy tumbling net cord shot. These shots can certainly touch the net or come close to it on the returner's side of the net. See this video for ample samples, and some examples of people returning these shots.

In the official Laws of Badminton, there is no rule saying that whoever hits the shuttle last into the net loses a point. The relevant rules are (emphasis mine):

§15.1 A shuttle is not in play when it strikes the net or post and starts to fall towards the surface of the court on the striker’s side of the net.
§15.2 A shuttle is not in play when it hits the surface of the court.

§15.1 does not apply here since the shuttle touches the net on the returner's, and not the striker's side. So if B is unable to return the shot, then it's simply a point for A because the shuttle lands within the court boundaries.

In real life, this shot does not require force but control, and is thus played with the strings rather than the frame.

A has another problem though: Since the shot completely destroys the shuttle, it's going to be a let:

§14.2.4 It shall be a let if during play, the shuttle disintegrates and the base completely separates from the rest of the shuttle.

If you hit a shuttle really hard, it won't disintegrate right away; top players do that all the time. But shuttles will break much faster the harder you hit.

However, the resulting shot of hitting with a lot of force is a very fast smash, and definitely not tumbling. Drag grows quadratically with speed, so the forces acting on a shuttle to stabilize are much stronger for fast shuttles.

So why not have A be able of very fast smashes, faster than B can react? This moves the ability from fantastical (which is fine if you're aiming for a Dragon Ball or Harry Potter style, but strange if the novel is set in real life) to something that is certainly possible:
Usually the fastest smashers are professionals, but it is absolutely not unheard of for strong amateurs – or professionals who lack in other areas of the game – to get the timing and technique of an extremely hard smash just right. Maybe A has this timing down, trains smashes all the time, has the perfect arm length, and does plenty of relevant strength work in the gym.
This allows you to not alienate badminton-aware players, keep the Birdkill name, and have A have a finishing move (although maybe B can find a strategy to negate this?).

Alternatively, A may be an excellent net player, somebody who can play excellent tumbling net shots, maybe tricking their opponent as to whether the shot is going long-line or cross. This keeps the results of the shot you envision, but it does not destroy shuttles, and the player archetype is more of a trickster rather than brute force guy, even if in real life net shots requires a lot of repetition too.