Higgins was looking at videos coming out of the Daraya region when he noticed several weapons that he had not yet documented in Syria, among them a portable anti-tank rocket and a wheel-mounted recoilless rifle.
Source- New Yorker https://www.newyorker.com/magazine/2013/11/25/rocket-man-2
It seems to me that the entire noun phrase is modifying weapons. So it cant be an absolute phrase.
Isn't a noun phrase modifying another noun an appositive
According to Huddleston & Pullum (2002), it is a verbless clause acting as a supplement (pp. 1265-1268, 1359-1360); essentially it's similar to that in your previous question, but we don't have a verb in the -ing form.
That verbless clause instead consists of a predicative complement (sometimes called a subject complement) "a portable anti-tank rocket and a wheel-mounted recoilless rifle" and a subject "among them." These have been reversed in order due to subject-dependent inversion (ibid., pp. 1385-1386).
Here you do indeed have an absolute phrase:
Higgins was looking at videos coming out of the Daraya region when he noticed several weapons that he had not yet documented in Syria, among them a portable anti-tank rocket and a wheel-mounted recoilless rifle.
It’s hard to see because its subject is inverted and because being is deleted (which we can do with absolute phrases). You can look at it like this before putting it back the way you had it:
He noticed several weapons that he had not yet documented in Syria, a portable anti-tank rocket and a wheel-mounted recoilless rifle
beingamong them.
