He didn't cut the word off at the end to censor himself or the joke in any way. He did it to further the joke. I would argue that even if he did say the whole word--although it would be less funny--it would be justifiable because he was not being serious.
Well, yes. But like it or not, and he knew it, and you know it, there would be some portion of the community that didn't get it, and that thought it was a bad way to end things. They might even say "I get that he was trying to make a joke, but I don't like that he used that word to make it." So he made the joke that somehow his piece was being censored by a third party. That made the joke work, like his multiple "Freudian slip" references to man love followed by the quick disclaimer "I'm not gay!"
Your other examples are laughable. Bastard? Lame? You can't be trying to make the claim that "barbarian" is as offensive as "nigger," as though to say any derogative discriptors are ALL EQUAL. The words you speak of fall into the category of words that may have been offensive once (doubt it with "lame," but "bastard" and "son of a bitch" would be cause to duel TO THE DEATH - no joke, if uttered seriously only 200 years ago), but which are not now. This has been discussed here, though not at length, so have away if you like.
Remember that this whole dialogue began because Yahtzee has been making the same sort of joke: "I'm not gay," ie the ironic "I'm not homophobic," in other threads. A member here took those seriously to mean that maybe he really is homophobic and that it is offensive. I am defending his use of gender-identity-themed humour, and even of race-themed humour. I think still that he doesn't have the license openly to use the word "nigger," because it is still currently an offensive word, no matter what Quentin Tarantino may think. Trying to create fictions where white people use the word and it is tolerated by their black friends, as Tarantino does, does not ring true. Yahtzee knows this so even when he has black-faced Spiderman say "Oh Lawd I is Gonna Rape Me Some White Wimmin," he still knows not to utter openly a word which is troublesome to the better part of the black population (at least it is here in North America; who knows what they think of it in England).
Barbarian does not reference the Barbary Coast, by the way. It simply means "foreign." The Barbary Coast borrows its name from the same word, but "barbarian" has an independent origin, and "barbarians" can come from anywhere. And of course now the word has virtually no meaning; nobody calls any groups of people "barbarians" anymore. The word is more likely to evoke a memory of pop fantasy than anything else. But while you're at it, say you said "I was gypped," to mean you were ripped off in a deal. Likely you wouldn't offend anyone, not even folks of Gypsy descent. But "I was Jewed" would probably offend someone. You might get away with that however if you were Jewish and everyone hearing you knew that. Some words were offensive once to some people and they are not now, etc etc etc.
"I had a lot of different ideas. At one point, Luke, Leia and Ben were all going to be little people, and we did screen tests to see if we could do that." -George Lucas, in STAR WARS: the Annotated Screenplays (p197).