Symbolism, Imagery, Allegory
The duel in From the Earth to the Moon isn't exactly an epic battle—we're not sure either of these guys could pass for Jar Jar Binks, much less Darth Vader. Instead of a duel it's more like a do something else.
For his part, Nicholl is too busy saving "a little bird […] entangled" (21.42) by a spider to do much fighting. This emphasizes something that we already know: Nicholl, "a great manufacturer of armour-plates" (10.8), loves to protect things. But this also makes us like him a bit more, which is good since we've spent the preceding chapter distrusting him, and before too long, we'll be watching him prepare for orbit with his sworn nemesis, Barbicane, whom we like.
Barbicane, on the other hand, is "tracing formulae and geometrical figures in his notebook, whilst his rifle lay uncocked by his side" (21.63). Again, this illustrates something that we already know about Barbicane: He loves to solve problems. So although violence is usually a byproduct of his solutions, it doesn't seem to be ever be his intention. It's all about finding solutions for this guy.
Despite the fact that this duel doesn't end with a decisive victory, it teaches us a few lessons about both men as individuals, and when it comes to both of them, it show us how non-violent they each fundamentally are. It also helps them get to know each other—after all, the day ends with both men joining the same team. If there's ever been a time to rock out to "Why Can't We Be Friends?," it's right now.