It would need 8 arms, not 4. (A well-placed Knight meaningfully controlling all of its 8 target squares is actually referred to as an "octopus Knight" sometimes).

It is also opinionated, in the sense that the vectors for Knight moves is [2, 1] and [1, 2] (whereby in both cases negative numbers can be used)... so whether you visualize a Knight move towards the left top corner as an L (x-1 first, then y-2), or as an ꓶ (y-2 first, then x-1) is an arbitrary decision.

It might be my OCD side coming out, but any design prioritizing one of these perspectives over the equally valid alternative doesn't feel "clean" to me somehow : )