As indicated by the graphics, each square has a letter on it, a red pipe, and a black pipe. These pipes can either both go straight (one east-west, the other north-south) or they can curve (one east-south, the other north-west, for example). Each answer starts on a numbered square, and follows the pipe of the appropriate color until it ends in a boundary or a filled in square. Just as in an ordinary crossword each letter is contained in exactly two words.
Furthermore, as a bonus, each vowel is on a curved pipe, and each consonant is on a straight pipe.
The filled in grid is:
As you can see, there is one pipe which is unclued. The word that goes along those pipes is UNIDIRECTIONAL, which is the answer.
2006 MIT Mystery Hunt