I always thought of this bit of code as a great example of applied numerical methods techniques, rather than “Black Magic” The magic constant is derivable from standard methods and one can even choose to optimize other measures of error.
Unorthodox technique, that you can explain if you try hard enough (in a sense, everything that reliably work could be explained and someone has to came up with in the first place), used by people who don't really understand it.
I would consider “black magic” to be something that works reliably due to some specific and idiosyncratic property of the environment that it operates within. Basically, something that is exceptionally tightly coupled. I think the novel FPGA solutions that genetic algorithms can create fall into this category; they often didn’t work on different boards, or even when the same board was plugged into a different power supply because the solution was overfit.
The legend himself, John Carmack.
Fast inverse square root is really the perfect example of black magic in programming.