A patriot is not just some guy who is good at football. It's a person who loves their country so much that he or she would fight to protect the rights and freedoms that the country values. In “O Captain! My Captain!,” Whitman celebrates the bond that patriotism creates between the average citizen and the leader of the people. The captain is portrayed as a patriot who has risked his life in some mission for the people on shore. The masses on shore celebrate the captain's success, and the ship’s return, with all the trappings of patriotism: flags, bugles, and bells. (Remember that this poem is set before American flag lapel pins were invented.)
“O Captain! My Captain!” is a star-spangled, patriotic poem, rather than a flag-waving nationalistic poem, because the poem presents a general feeling of love for one’s country, rather than a loyalty to specific ideas about enemies, allies, or the rights of citizens.
The poem is not distinctly American in the sense that just about anything in the poem could apply to any country in the western hemisphere in the mid-1800s. But the exact context in which the poem was written (the assassination of Lincoln) does make it an “American” (not a vampire) poem.