In the film, this giant mechanical gorilla was created in Nevada, designed after the legendary creature called King Kong. While being tested, energy radiated off the mech and mutated a bird into a giant creature. The monster was dubbed "Archaeopteryx". Archaeopteryx fights Godzilla in Las Vegas, where the giant bird is killed by the king of the monsters.
There's concept art for the battle here ->
It's worth noting that the monster is labeled as "Gigamoth C" in the book he was discovered in. Perhaps he was also considered to have some role in Godzilla vs. Gigamoth. But as you can see, it CLEARLY isn't a moth.