I don't think its the accent and speech itself that makes him not stutter. Stuttering is psychological (in most cases) and related to the stutterer's self image and ego. The guy in the video is playing a character (acting). When he does that he is disconnecting from his own ego and immersing himself in the character that he is impersonating. That's why he's not stuttering. This is the reason why so many actors who stutter, stop stuttering when they go on screen and act. Because they completely forget about themselves and focus on the character that they are impersonating. This is my take on it.