The way I see it, Gambol just happened to be the guy to speak up first, and it just escalated. Let's walk through their dynamic in this scene:
Edgy clown barges into a meeting full of crime lords dressed exactly like the wackjob who stole their money. It's reasonable for Gambol or any of the other mob bosses to put Joker down. Gambol gives Joker a chance to beg for his life. Joker flippantly suggests a magic trick instead. Gambol sends his right-hand man to handle the Joker, whom Joker KILLS as part of the "trick."
Joker may have impressed the others, but clearly at Gambol's expense. Joker then gloats about the money he stole from them. Gambol gets up to kill Joker but stops out of respect for another mob boss's request to hear Joker out.
Joker starts to explain the deal very disrespectfully, so a vexed Gambol interrupts him: "Freak." Perturbed, Joker goes on to demand a ridiculous fee ("Uh, half") for the ridiculous service of killing Batman. The others laugh it off, but Gambol, in no mood to laugh, calls him "crazy." A little pissed off by that second remark, Joker decides to belittle "little Gambol" by name.
Gambol gets up again and is only stopped by Joker's bombs threatening to kill EVERYONE present. Everyone is scared by or angry at the Joker at this point. Gambol sets a bounty on Joker's head. Anybody could have reasonably done so, but he took initiative because he was insulted the most.