The guy started the video by saying the dog is evil, and as such he made it react to the most evil things he could think of. Many Jewish comedians here in the UK and across the world have come out in support of him, so its not as clear cut as you are trying to paint.
I'm not trying to paint anything as clear-cut.
As far as I can see, the prosecution see someone using comedy as an excuse/cover to voice their extreme views. And the defense says the comedy's the point, and the anti-semitism is just for effect.
I know David Baddiel has spoken in support of this (not sure about any other Jewish comedians?) and I've seen a clip of him discussing it with Ricky Gervais. The main point is that he feels, like you, that the guy's descriptive intro explicitly makes it clear this isn't anti-semitic, and he just wanted to make the dog say the most evil thing possible. Also, the dog is funny, and no topics are off-limit for jokes.
But clearly the prosecution disagree that prefacing something offensive with a statement distancing yourself from the content (it's just for effect, it's just a joke) is a watertight disclaimer, and that there's genuine malice, or whatever the legal definition is, in the deliberate use of that material. Whatever you claim your agenda/intention was can be factored into your defense, but it doesn't conclude the whole case.
One interesting thing about the Baddiel/Gervais clip is that Baddiel does a brief lead-up to revealing the cue phrase, and Ricky guesses it might be 'heil', but when Baddiel says it's 'gas the Jews', Gervais doesn't immediately laugh. He just sort of stops, then says 'oh... hold on', then 'right', but he doesn't start to show any amusement (Ricky Gervais, who laughs at every fucking thing) until Baddiel continues and makes it clear he's amused, that the whole thing is funny, etc. Then he kind of relaxes into it. It's just interesting to see the instinctive reaction to that phrase, even to Ricky Gervais, was.. what? A hesitancy as to whether you could laugh at it, or whether it was funny or awful? There aren't that many short phrases which have such power, even on comedians who'll say the most outrageous things.