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The word "snipped" can seemingly be used to mean "said in a snippy manner":

"No," she snipped, obviously annoyed

—http://rosemarinetheater.blogspot.com/2013/05/white-boy-can-rap-looking-at-benny-in.html

...the former president was emphatic. "No," he snipped.

—http://www.washingtonpost.com/blogs/post-partisan/wp/2016/02/03/no-bernie-sanders-is-not-barack-obama

"No," she snipped. "You're American, aren't you? You're not very popular here today."
—http://www.city-journal.org/html/london-peace-marchers-say-long-live-intifada-9989.html

Yet no dictionary (of the dozen or so I consulted) documents this usage. Not even the OED [paywall], which documents every obscure meaning every word has had over the past 500 years. Not even urbandictionary, in which anyone can add words and definitions with no editorial oversight.

Is this meaning too rare for dictionaries to document? It strikes me as a somewhat unusual but not obscure construction when I run across it. But of course it's difficult to google for a word used with a specific meaning when that word also has a vastly more widely used meaning. (You'll find a mix of hits and false positives searching for exact phrases such as "no she snipped," which is how I discovered the above citations.)

Is this meaning too new to have made it into any dictionaries? The oldest of the above citations is from 2003, and again, my sense is that it's been around longer than that (though again, without a way to effectively search, it's hard to say).

Is this usage actually an erroneous substitution for another word? "Sniped," for instance, can also be the verb in a dialogue tag, but it has a different meaning (one which could conceivably apply in the third citation above, but not the first two). I can't think what other word might be intended.

Has this meaning been collectively overlooked by all the major dictionary compilers? This seems extremely improbable, yet Sherlockianly correct.

Am I overlooking another possible explanation?

This is an interesting question, in the sense that it touches upon the matter of this site: what precisely allows some feature of language to count as ‘usage’.

You might start by asking a different question: ‘criteria for adding a word to a dictionary’. It’s not exactly your question, which is about new uses of old words, but it is a start.

Here is what Merriam Webster says:

Criteria for adding a word to the dictionary
To be included in a Merriam-Webster dictionary, a word must be used in a substantial number of citations that come from a wide range of publications over a considerable period of time. ... The number and range of citations needed to add a word to the dictionary varies.

That used by Oxford Dictionaries is broadly consistent with that. Of course, terms like ‘a substantial number’ and ‘wide range’ of publications and ‘considerable’ period of time. Infuriating as the vagueness may seem, it is inevitable: any boundary would be arbitrary and so possibly restrictive.

You should look carefully the idea of range of publications and period of time. The issue is more than the number of uses.

Nevertheless, OED, Merriam Webster and most major dictionaries are keen not to fall behind the natural development of the English language. So OED has a public site:

public.oed.com

It gives you detailed guidance how to engage and propose words/uses not currently cited.

It appears sniped and snipped are in many cases used interchangeably. Your reference American Dictionary:

snipe (snīp)

intr.v. sniped, snip·ing, snipes
1. To shoot at individuals from a concealed place.
2. To shoot snipe.
3. To make malicious, underhand remarks or attacks.

and the OED cites sniped

fig. To assault with harsh sly criticism; to rebuke or censure
sharply; to make a carping attack at (someone).

As in:

1979 A. Hailey Overload i. xiv. 79 The press representatives had
eaten and imbibed with gusto, then in published reports, some had
sniped at GSP & L for extravagant entertaining at a time of rising
utility bills.