Coleridge's poem contains many supernatural elements and on the surface seems to be a scary tale warning people not to kill anything in nature because all things in the world are interrelated. A seemingly isolated act can have ramifications that extend beyond a single person, as the Mariner tries to tell the wedding guest. In order to receive salvation for his thoughtless act of killing the albatross, the Mariner is doomed to tell his tale to whomever he meets. Some critics believe that the poem is a religious (Christian) allegory, but if one truly understands Christianity, one will realize that the viewpoint expresses uncertainty about religion. Also, it would not be up to a person to effect his salvation. Christianity emphasizes that salvation comes through faith, not through works, so no way would God condemn a person to tell his tale of woe in order to redeem himself.
The Bible does, however, instruct man that he is the steward of the earth and therefore must treat all creatures with respect. All creatures are not like man, however, who was created in God's image, and has a soul. So while man is steward of the earth, man himself is the most important creature and would not be punished for killing a creature, necessarily, unless, like the Mariner, it is for no reason. This act would be sinful, but would not result in eternal condemnation, as depicted in the poem.
There will be other views that will not agree with my view, but that is how I see it.