The pesky "a": Is there a linguistic term for this phenomenon?
Perhaps the term you are looking for [to explain the missing "a"] is "poetic licence".
Without the "a", there are 3 beats in the 1st part of the quote, "One small step for a'man", to match the 3 beats in the last part ["one giant leap for mankind"].
The "a" is the only word sound which is expendable.
In this case, tempo trumps linguistic precision.
We all know what the sentence means even if, as you point out, it doesn't exactly say what we know it means.
Everyone who witnessed the event knew this "first small step" was a milestone of history. We needed the words celebrating the event to sound like they had been spoken for all the ages.
Only poetry can accomplish this.
One can write poetry without rhyme, but not without rhythm.
If there had been 4 beats in the 2nd part of the sentence, the "a" would have been stressed, not muted.
