Think what I suggested "would have worked
if" - ah, wonderful words - the center of the magnet object had been where I thought it was instead of where it actually is (darn reality, even the virtual type).

Consider instead a torus with the center truly in the middle of the ring. Now the case you show will not count as a ringer since the center of the torus is more than a radius away from the wand (pole).
If you want to actually orient the opening so the horseshoe won't go through the pole when tossed, you do need to do more, of course - or you could just change the name of the game to "Ring Toss."