It is important to realise that in Part 33 of this excellent poem, the speaker takes on the voices of people that he sees as unsung heroes. Thus we are presented with the voice of a skipper in a storm, a mother burnt for a witch in front of her children and a firefighter crushed by a falling building, to name but a few. The stanza you are referring to was inspired by a real-life incident that occured in 1853. A ship was hit by a violent storm in the middle of the sea, washing lots of passengers overboard. The captain of another ship helped rescue the survivors. The heroism of the captain in saving the people from the first boat is highlighted in this stanza, by focusing on how the Captain "knuckled tight and gave not back an inch":
And chalk'd in large letters on a board, Be of good cheer, we will not desert you;
How he follow'd with them and tack'd with them three days and would not give it up,
How he saved the drifting company at last...
Thus the Captain is a suitable figure to be identified as an unsung hero in this section of the poem, given his bravery and his faithfulness to the task at hand, even in the face of danger. Note too how Whitman identifies with the Captain, as he says in one of the most famous lines of this poem:
I am the man, I suffer'd, I was there.
This phrase somehow makes the scene that much more immediate and shows the compassion and empathy of the speaker, whilst highlighting the bravery of the Captain.