The thing that rubs me the wrong way about this is his tone. He seems to convey that people who associate the swastika with things other than Nazism are pretentious jackasses. That seems condescending and culture-centric to me.
For context, imagine yourself in Revolutionary France, where the Royalists roamed the countryside battling the Republicans, terrorizing and pillaging along the way. The Royalist emblem was a plain white flag, considered internationally as a symbol of surrender. Were you to wave a white flag in Britain, it would hold one (basically benign) meaning, whereas if you were to wave a white flag in France, it would hold an entirely different, politically-charged meaning. Is either interpretation of the symbol intrinsically less valid or appropriate than the other? I shouldn't think so: each has a meaning within its own contextual history, and the people who ascribe each meaning are doing so reasonably.
That said, I agree with the overall ruling here. In the above example, the issue that arises is born of appropriateness of audience. Pictures of an open autopsy subject would be considered reasonable for a textbook in an anatomy class but be considered horrifying for publication in a newspaper for general circulation. Similarly, a swastika as portrayed to a Western audience would conjure associations to Nazism to the vast majority of players, and only in South and Southeast Asia would that pattern change. I'm certainly not one for banning symbols that could potentially be seen as offensive to some people (I think Nintendo's '90s policy of not featuring crosses in their games to avoid associations with Christianity to be ridiculous), but when the majority of Westerners can look at a symbol and from that the first memory drawn forth is that of that culture's biggest villains and mass-murderers? Perhaps a bit of temperance is not uncalled-for.