Thanks for pointing that out. I will definitely have to reword a few things on our site. Maybe the same 'essential' mechanic, or something to that effect.
The king could still move the same two squares in the direction of the rook, but it might mean that the space is sometimes occupied by the rook or you may be simply jumping over the rook.
I can later (short on time this morning), and I plan to add diagrams to the website and a video discussing it.
Basically, the rook, assuming the spaces are open and he and the rook havent moved, either moves adjacent to the king (if he isnt already adjacent) and the king moves two spaces around him.
Chess 960 was done to address memorized openings and,to a certain degree,the issue of draws.
But Chess960's castling mechanism is totally unintuitive. So, Chess 744 was born. The exact mechanic (rook moves to king and king swings behind it) from standard chess is used and all of chess 960's setups that had a rook and the king in a corner were removed. This website goes into detail. There is no better method, IMHO, of creating an intuitive chess variation that addresses this issue. It is very hard and unintuitive in Chess 960 to remember where to move your pieces to castle and whether or not it is even legal given the squares the king has to move through.