I think people with any sort of predisposition to be offended are bound to get burnt by Yahtzee at some point. That's okay - I think we're probably all doomed to having something we find objectionable even in humour - but the key is realising that this is bound to happen.
To those of you who are finding yourself calling Yahtzee in some way prejudiced towards some groups of people, I implore you to look back on his works. He makes fun of everyone, whenever the context requires it, because his 'job' is to make fun of things.
Evidence: While not an accurately complete portrayal of the whole world by a long shot, I distinctly remember a review (Paper Mario, for the curious) wherein he called the Japanese xenophobic dicks, Americans arseholes and mocked Australia as consisting of sheep (the animal, presumably) and himself.
ZP, simply, is not politically correct, and doesn't in any way strive to be. Enjoy it as what it is. If it offends you, that's all right, but please keep the above evidence in mind before you draw conclusions about Yahtzee (or the editors, or even Zero Punctuation as a whole) from that.
As for the censorship: I don't mind it. I don't think anyone at the Escapist (or Yahtzee himself) ought to feel obligated to (un)clean this video for us to we can enjoy it without the bleeps. This was not made for the ZP audience. It is simply being courteously shared with us - or so I gathered from the alert.
As to my personal opinion: bees. Can't stop laughing. Sides hurting. Argh. *splits into several Tetris-shaped blocks that scatter across the floor*