So basically just a shortest path algorithm starting from the player to all other tiles?
This gives you a value (distance to player) for every square on the board; you can do a lot of things with that data, like choose between multiple "best steps" based on some other preference, or choose "best steps" for a large number of monsters efficiently.
If the player's route is not straight, some squares with "fresher scent" may be physically more distant from the player than squares with less fresh scent.
The algorithm is summarized in the article as: "When an enemy enters the Chase state it tries to raycast to the player and if nothing is in the way - chase em! If something is in the way, it goes through the scent trail in order and tries to raycast to each scent until it can see one, then - chase it!"
With complex geometry, this will frequently lead to a non-optimal route, and is probably more fun to play against.