I discuss Charles Bloom's 2011 article in some detail on my page. The original "magic" kernel (i.e. [1,3,3,1]) can be rightly categorized as just many things. It's the generalization to the continuum case, and the addition of the Sharp step — and, now, to arbitrary higher "generation" 'a' — that makes it useful and more powerful. Bloom's post ten years ago inspired me to play some more with the "original" and figure out at least the "continuum" version.
I recommend you check out the paper http://johncostella.com/magic/mks.pdf for developments since the original 2006 "magic" kernel. :)