I can't be so sure that Jet really does snap that guys neck, but he looks like he wants to real bad.
Anyway, this is my take:
Jet, when he's exacting punishment on the two syndicate goons chasing Maifa, shows a violent side that we are not accustomed to seeing. Jet's tenacity is legendary, but there should be a psychological barrier that stops him from taking the final step, that should stop him from taking the final step. What triggers this barrier, and, more importantly, what would make Jet cross the line?
The pure savageness with which Jet strikes at the goons is something we don't see from Jet until this point. One aspect of this is that Jet would have a natural aversion to all things dishonorable, such as the syndicates, and there is no doubt that the underworld directly led to his loss of limb and self-confidence. At the same time, Jet initially refuses to chase after Udai when he is approached by Fad. Wouldn't he want to go after Udai solely on principle? Yet, that isn't how it happened. For that matter, when Jet lashes out at the goons there appears to be at least a moment where Jet is out of control: something completely out of character for a man known as the "black dog."
Perhaps, Jet's paternal instincts (or maybe that little bit of "mother" bear in him) are taking over. Sense of honor would dictate that Jet take Maifa under his protection. But, Jet isn't in the driver's seat of this adventure; he spends most of his time about a step and a half behind her and the awkward sexual chemistry that is exacerbated by Spike, Faye and Ed makes Jet uneasy. That means there is a conflict between what Jet needs to do and what he can do. It becomes that much harder for Jet to protect her if he can't even control what they are doing or where they are going.
Would he kill to protect her? Killing is the domain of the syndicates and their assassins. He doesn't make much of an attempt to kill Udai in Black Dog Serenade, a hesitancy that might be attributed to distaste. Of course, that's a different situation since there Jet is still in control of the moment: Udai's gun maybe aimed at him, but his response to whatever Udai does is already mapped out in his head. When Maifa finds the stone, she loses track of the goons but Jet does not. Still, he is on a street with limited avenues of escape, and a confrontation with the goons is unavoidable: this is the moment where he has to face his limitations.
If he really does break that guys neck, then there's a whole new set of questions.