The rules don't cover this situation, so it's up to the DM.
The adventure module can include a specific rule covering this situation, if the writer so choses. This may be the best option.
However, what this particular situation is essentially asking the player to do is to throw an object within 10 feet of a character, an exceedingly easy task that may be so easy as to be an automatic success. You're hitting a target of a circle with a twenty foot diameter. It's literally like hitting the broad side of a barn.
Additionally, it doesn't actually matter which direction it misses in, since the rope moves toward the character anyway, so the only factor which counts is distance. It's very difficult to miss a throw by more than ten feet, given that the rope of climbing's length is 60 feet, so the target must be within sixty feet.
Even hitting a human spot-on is AC 10, but then it's even easier than that because the target wants to be hit and is, presumably, actively attempting to be hit. The chance of failing to make a direct hit in this case is relatively slim. If a one-round delay causes the PCs to fail, then it won't matter how badly you miss, so measuring miss distance is irrelevant.
Also, bear in mind that player characters quite frequently do not do the obvious things. They may not know how the rope of climbing works (if it can be guaranteed that they have it, it's presumably given on the adventure, so it's new to them), and may not think to use the solution that's obvious to the adventure author.
