Both times he used it, he's giving up on getting somewhere and is just screwing with the guy; it's not part of his main argument.

It's worded like an argument. And he and the bystanders would, when listening to it, believe that Eliezer had made an argument that nobody was able to refute. The impact of Eliezer's words depends on deceiving him and the bystanders into thinking it is, and was intended as, a valid argument.

In one sense this is a matter of semantics. If you knowingly state something that sounds like an argument, but is fallacious, for the purposes of tricking someone, does that count as "making a bad argument" (in which case Eliezer is using the Chewbacca Defense) or "not making an argument at all" (in which case he isn't)?