The "veneer of civilisation" is threatened by the "brute within" through the realisation that man is actually rather insignificant when it comes to the powers of nature, and nothing about him--his strength, his intelligence, what he has managed to achieve in life--will protect him from the much greater force of nature. The "brute within" can therefore be seen in the following quote from the sixth part of this short story:
...it may be remarked that a man would conclude that it was really the intention of the seven mad gods to drown him, despite the abominable injustice of it. For it was certainly an abominable injustice to drown a man who worked so hard, so hard. The man felt it would be a crime most unnatural. Other people had drowned at sea since galleys swarmed with painted sails, but still--
Note the way that the correspondent, even though he admits that others have drowned throughout history, still believes that it would be a "crime most unnatural" for him to drown, and it would be an act characterised by "abominable injustice." Even though he has worked "so hard, so hard," with the repetition emphasising the effort, it is clear that this is no guarantee whatsoever of survival, and indeed, it appears, through the death of a oiler, that natural strength and knowledge does not give you a greater chance of living, as the correspondent, who knows very little about the sea and is not as strong as the oiler, survives whereas the oiler does not. The "veneer of civilisation" is therefore stripped away by the "brute within" through the realisation of man's insignificance and powerlessness in the face of nature.