Does "the N-word" have implications other than a word used for racial discrimination?

Yes, "The 'N'-word" means nuclear in this specific case.

No, it doesn't have a general meaning other than of n----- 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.

I believe you are correct: N is for "nuclear".

There have been many articles written about Iran and its nuclear programme, aspirations and possible intentions. The author is obliquely remarking that it seemed impossible to omit a reference to this work in any article about the country. It appears that every article written must include the word nuclear.

However, he harboured a suspicion that there must be some article he could write where it would be possible not to use the word nuclear, and having written that article, he added a footnote to that effect. Even with the footnote, he still didn't use the actual word itself.

He means "nuclear".

When we want to refer to a word without actually saying it, we often refer to it as "the [first letter]-word". The audience is expected to infer what the word is from context. We usually do this to avoid breaking taboo but, of course, it can be used for humorous effect. For example, an anxious student might ask his friends not to use the "e-word" ("exams"). In the context of the New York Post article, it's clear that the journalist means "nuclear", not "nigger".

As an aside, I first hear the phrase "the n-word" being used by liberal Americans, and it struck me that the usage was a little strained. Their attitude seemed to be,: "if we keep treating the word 'nigger' as if it's too shocking for normal use, then soon it will be". It looks like they succeeded.