I've never understood that quote as I believe it removes a necessary word. "Needless" describes the type of word to delete. Without it, isn't William Zinsser suggesting we should omit random words?
No.
Without an explicit predicate, I would guess that the implicit predicate would default to either "true" or "false" rather than "at random". If it defaulted to "false", then the imperative conjugation would make no bloody sense at all (i.e. "eat up" would parse into "don't eat anything"), so I think he's saying you shouldn't write anything.
I disagree, I find "omit all words" to make as little sense as "omit no words". Personally, I find it more likely to default to "omit some words". This, of course, does not describe the type of words we should be omitting, but rather that there exist words that we should omit. Saying "omit needless words" does describe the type, adding more information which is not there otherwise, making it a "needed" word.
I always read it as a joke with meaning. "Needless" within the context is a 'needless' word. =)
I agree, it's supposed to be a joke claiming that 'needless' is a needless word. I'm saying I do not understand the joke because I believe 'needless' is actually a necessary part of that sentence.