but that's not how it's being used. what length of rope does it take to go around a quarter mile track? there's no ambiguity even though the track has length and width. the dimension in question was specified already, the width of the crack, so referring to the measure of that as its length is fine, no ambiguity.
Your sentence is dramatically better than theirs because you're referring to the length dimension of the rope and the track. "What length of rope does it take to go around a quarter-mile wide track?" <- using the author's mistake in your sentence. There's not enough information in the sentence to answer correctly.
The correct word for a measurement of wideness is width.
Length [NOUN]:
1.
the longest extent of anything as measured from end to end:
the length of a river.
2.
the measure of the greatest dimension of a plane or solid figure.
It's pretty unambiguously wrong. You can back into what the author meant without ambiguity, but that doesn't mean the author used the correct word.