Yes, if taking it seriously, then those are reasonable conclusions. However, I think you’re just overthinking it, in this context the scenario exists to service the joke rather than the other way around.

The comedic implication is that the giant eagles are natural predators of goblins and, more importantly, hobbits. And might be inclined to a mid-flight snack.

Well, we know that they’re typically referred to as male (as far as I know at least), so perhaps they’re all transmasc?

Of course Anne of Green Gables is set in PEI so really it should have been set there. It would have been even funnier since they could probably outnumber the current population pretty easily if they immigrated en masse.