Indeed, a double-move Knight with 'Lion power' is an immensely poweful piece. And it does hit-and-run captures from a distance, along a step that almost no piece reciprocates.
That people have to think harder is not really a valid objection. This is supposed to be a difficult variant, and having them think harder is the entire objective.
Of course black's weakness is that he only has two pieces, so he can never afford to lose any of them. When white keeps his King out of range of checks from squares he does not attack, and keep all his pieces protected, he does not have to fear two-step captures. So he only has to worry about hit & run captures.
Ok. Well, that had to be clarified in the OP. I'm assuming it might have been somewhere in the long discussion that I haven't read yet, but my previous understanding was that there was no such modified rule of checking, which lead me to the conclusion that a Knight's otherwise check would be considered checkmate; I wasn't quite sure why I was "incorrect again", as stated legoPirate.
With this new knowledge, I say, the problem is that one can't always spot it when White is in Check, since people never had to, as a rule, see Knight moves 2 moves down the line; compound with the fact that it's simply frustrating how White's King is restricted: he can't move onto a square 2 knight moves in addition to the original check 1 knight move away.
Where then can he move? It's almost like playing against a piece with a 7x7 area attack. (That's the High Priestess's 5x5, plus 1 range!)