I don't think so, in this case. We weren't asked anything about completion of an ESTA or API. It definitely felt like more of a security/behavioural screening

I don't think so, in this case. We weren't asked anything about completion of an ESTA or API. It definitely felt like more of a security/behavioural screening - not a check on visa or travel eligibility. If this was the case, they'd have made their intentions clear and wouldn't have been at the gate waiting to re-check passengers. Or that check would have been performed at the check-in desk, where they check your eligibility to travel (correct documentation, tickets, etc). I do suspect, however, that they're contracted by the airline. They weren't in any other airline's check-in queue and we've never seen them in the past (this was our first time flying AA).