This means that the Rook only gets to move in 6 directions (up and down in addition to the 2D moves).
The true 3D diagonal, from 1a1 to 8h8 via 2b2, 3c3, and so on, is not even a move according to this mapping.
The overly mathematical approach driving the several inventors of this mapping always leads to poor game design for reasons that go beyond whatever faults there may be in the mapping itself.
For example, in the Kogbetliantz Game, the ratio of space to force is much greater than in Chess, many new pieces have been added, the initial position has doubled Pawns on the first rank, and in order to checkmate the bare King, you need 25% or more of your initial material (in other words, almost all games between masters would be drawn because it takes a large margin of victory to win the game).
Just because the games that use this mapping are "bad", that doesn't prove that the mapping is "bad". Furthermore, both times when I say "bad", I emphasize that I mean bad in the sense of being chesslike, because today I am looking for 3D Chess.
Perhaps all of the other 3D chesslike games are good and entertaining to play, although of course they should not call themselves "3D Chess". (My own opinion is that their designs are flawed, but I don't intend to try to prove it. Mileage may vary.)
However, the fact is that the old mapping really is very bad if you are looking for 3D Chess. A Bishop that moves straight down a file? This is chess????