The answer is that it was staged, and fairly obviously so. The clip even features cutaways to audience members reacting in horror to what is transpiring, not to mention a handheld shot of Kimmel being loaded into an ambulance -- directorial touches suggesting that the "incident" was thoroughly planned and rehearsed, not accidental.
A Wikipedia entry devoted to the show describes that night's episode as follows:
In an episode that originally aired on May 15, 2006, Kimmel staged a stunt on his show whereby a rattlesnake bites him on the hand. At first it looks real, but as it progresses, there are clues that it is faked. The show follows Kimmel as he is taken to the hospital. After a commercial break, continues to do the show from his hospital bed with the band, having traveled in the ambulance, at his bedside. The rush to get him in the hospital tied in with his guests from the ABC show, Grey's Anatomy. At the end of the episode, the rattlesnake talked while the credits rolled.