I can give an explanation as a law student. In continental European law there is an institute of "Extreme Necessity" which has a variety of requirements that when all met make a crime nonexistant. Most importantly it is allowed to sacrifice good of another that is less or equal in value than the good being saved. It sounds weird but it really does make killing somebody in order to save oneself legal (provided of course that it was really the only way to save yourself). The case of whaleship Essex is a textbook example of this institute in Civil law.

In US and UK things are even more simple as necessity as a defence is widely accepted as something legitimate. Requirements for it aren't strictly written and quote:

"The cases and the literature suggest three essential elements of the defense of necessity: (1) the act charged was done to avoid a significant evil;(2) there was no other adequate means of escape; and (3) the remedy was not disproportionate to the evil to be avoided."

As it is clear that all 3 requirements are fulfilled and even if crew were charged they would probably be let go. But that is just usually so. Since conditions aren't strictly prescribed in common law choice of values can play a very important role. In a similar case of Regina v. Dudley and Stephens three crew members were convicted for killing a cabin boy and eating him after eighteen days without food.

"Commentators have suggested that the defense based on the principle it is better for some to live than for all to die, is valid in both England and America, but that the question is confused in England because of the element of cannibalism"

This case and one more kind of similar (explanation given in the cited material) are all that could make a necessity defense invalid in US. But in both cases chosen values were what tipped the scales form dropping charges to convicting the survivors. In both cases sentences were mild (six months of prison) and that shows that in the case of Essex where crew was in worse conditions that lasted much longer their actions were even more justified and deserved not even placing charges.

I hope I won't get deleted for answering as a lawyer and not as a historian but from the law point of view it is quite clear why the crew wasn't punished.

Source:http://scholarlycommons.law.northwestern.edu/cgi/viewcontent.cgi?article=5903&context=jclc