The "Battle Royal" is probably the most memorable and pivotal scene in the novel. As you've guessed, the scene operates as a metaphor for a larger idea that Ellison wants to present about how black men, in particular, operate within a power structure in which white men are supreme.
The narrator introduces his memory of the battle by talking about conduct. The narrator learned from his grandfather, "a quite old man who never made any trouble," how to behave (Ellison 17). The narrator had made a reputation for himself as "an example of desirable conduct," a reputation that unsettles him because he suspects that it is the opposite of what white people actually want (17). He surmises that they would actually prefer for him to be "sulky and mean," but he chooses to be upstanding because he is afraid to act any other way (17).
In this recollection, we see that, as a young man, the protagonist's sense of identity is completely determined by the white gaze. There is already a sense of himself as a spectacle. When the white male spectators force the boys to watch a nude, blonde white woman dance, they make a spectacle of black male sexuality. When they force the confused boys to stay in the ring, while threatening them from their seats in the audience, they make a spectacle of their fear and powerlessness. There is a reminiscence here of instances in which slave masters pitted slaves against each other in crude boxing matches, forcing them, at times, to fight to the death.
On the surface, the blindfold may be a plot device that heightens the tension and desperation of the characters in the ring. Metaphorically, the blindfold symbolizes the way in which black men fight against each other in the interest of surviving (in the case of Tatlock) or of achieving recognition (in the case of the narrator) in a white man's world. This desperation is more vividly recreated in a subsequent scene in which the young men crawl around the floor of the ring, picking up coins and greenbacks thrown in by the white spectators.
It is not clear if the narrator is really "different" from the others. The only other fighter who is presented is Tatlock, the narrator's final opponent in the ring:
"I found myself facing Tatlock, the biggest of the gang....His face was a black blank of a face, only his eyes alive -- with hate of me...I wanted to deliver my speech and he came at me as though he meant to beat it out of me" (Ellison 24).
Tatlock is a man who has internalized racism, who sees the narrator as an enemy because white supremacy has taught him that it is another black man who stands between him and the resources that he needs to get along. While the narrator remains focused on his speech (incidentally, inspired by Booker T. Washington's ideas on self-reliance and social responsibility among blacks), Tatlock is one who has eschewed language in favor of physical violence. In other words, he has become the "sulky and mean" brute the narrator is trying not to be.
The narrator is not really "different" from the others. His goals may be different but, like the other young black men in that ring, he has no individual identity that is recognized. He must also co-exist with them in a power structure that renders them not only invisible but also desperate and, ultimately, powerless.