Yes, "The 'N'-word" means nuclear in this specific case.
No, it doesn't have a general meaning other than of niggern----- and variants thereof.
There is a general use of "The '[letter]'-word" to mean "The word beginning with the given letter, that I do not want to mention", most often with expletives like "The F-word" for fuck, "The C-word" for cunt and so on, though the less offensive the word, the less likely one is to use this form (so "The S-word" for shit is less likely, and so on).
In this case the author's reasons for not wanting to use the word nuclear is not that it's offensive in itself, but that it so dominates current discussion of Iran, that "to write a column about Iran without using" it, would be rare. By extension, to have other aspects of Iran even considered is relatively rare (in New York publications, at least).
Use of this form with words that aren't offensive in themselves is normally at least partly tongue-in-cheek. It also stops the claim being self-defeating; if he'd said "It may just be possible to write a column about Iran without using the word nuclear." then he would have used the word nuclear and hence proven himself wrong.
The tongue-in-cheek humour helps make it a piece of satire; he's not just saying that reportage on Iran is dominated by this one topic, but using satire to criticise this way of thinking about the country.
So, it's not a general use of "The 'N'-word", so much as a general use of the pattern it is an example of. That he would have been aware that the expression had a more specific use where it refers to a word considered offensive in itself, would have added to the tongue-in-cheek humour of phrasing it that way.