When I say "forward half of the Knight", this means that a White Forfnibakking can go from e4 to d6 f6 c5 or g5, but *not* from e4 to c3 d2 g3 nor f2 -- those moves are somewhat more backwards than forwards, you see.
Here is a complete example of its power: from e4, a White Forfnibakking can go to c5, d6, f6, g5, f4, f3, e3, d3, or d4.
This piece is as strong as a FIDE Bishop, and at most a tiny tiny bit stronger. The sideways parts of the King move (from e4 to f4 or d4) are what make it stronger than a Knight.
You will notice that the Forfnibakking has special advantages and disadvantages. In the endgame, it might have trouble tackling an enemy passed Pawn, and in the midgame, it might have trouble retreating from a difficult position. On the other hand, it always defends any Pawn that defends it, and at the same time covers that Pawn's advance.