I think the instructions should be: Move to the square indicated below the board without moving to a square the queen can capture and without capturing the queen. Once accomplished a new square will be indicated. Repeat until all possible squares are done.
Thank you! Once I saw this comment, very satisfying puzzle. At first I was fumbling my way through randomly, but around halfway I started to visualize the board as two "sets" of connected paths and grokked how to switch between them using the lower-right quadrant.
Exactly this - I used the upper right quadrant to switch lanes, but the idea is the same: if you cannot reach the target in the current lane, switch lanes and try again.