But why can't a bishop from d1 move to A4 and what am I still overlooking here?
It can move from d1 to A4. Here is a diagram I made for my Reroute66 page yesterday:
Should the description consider the following knight moves?
Knight on b3, is the move to a5 possible, because on the same diagonal?
By your rules, I think it is not legal. By Reroute66 rules, it is legal, and I have illustrated it in a diagram on that page.
Or a knight on a3, are the moves to a5 or b5 possible, because on the same line?
I have also illustrated this on my Reroute66 page, because they are legal in that game.
Chess66 uses a different rule for Knight moves than Reroute66 does. Mine says that a Knight can leap directly to any non-adjacent space reachable by any combination of a single lateral and a single diagonal move. Your rule says that a Knight may leap two spaces away to any space not on the same line, row, or diagonal, which I assume are all meant in a geometric sense. While mine specifies the types of moves, yours does not, and it replaces this with a stricter restriction on which spaces a Knight may leap to. Besides excluding moves to non-adjacent spaces, it also excludes moves to spaces in the same row, line, or diagonal.
Since both rules would give you the Knight's usual moves on an 8x8 Chess board, this doesn't provide a basis for comparison. I favor the rule I use, because it allows the Knight to gain some additional powers of movement around a Switch. By making the Knight an inverse of the Queen, as your rule does, it weakens the Knight around the Switches, which I don't think is fair for what is already the weakest piece in the game.
It can move from d1 to A4. Here is a diagram I made for my Reroute66 page yesterday:
By your rules, I think it is not legal. By Reroute66 rules, it is legal, and I have illustrated it in a diagram on that page.
I have also illustrated this on my Reroute66 page, because they are legal in that game.
Chess66 uses a different rule for Knight moves than Reroute66 does. Mine says that a Knight can leap directly to any non-adjacent space reachable by any combination of a single lateral and a single diagonal move. Your rule says that a Knight may leap two spaces away to any space not on the same line, row, or diagonal, which I assume are all meant in a geometric sense. While mine specifies the types of moves, yours does not, and it replaces this with a stricter restriction on which spaces a Knight may leap to. Besides excluding moves to non-adjacent spaces, it also excludes moves to spaces in the same row, line, or diagonal.
Since both rules would give you the Knight's usual moves on an 8x8 Chess board, this doesn't provide a basis for comparison. I favor the rule I use, because it allows the Knight to gain some additional powers of movement around a Switch. By making the Knight an inverse of the Queen, as your rule does, it weakens the Knight around the Switches, which I don't think is fair for what is already the weakest piece in the game.