If it was related to a demon contract, Elluka and Gumillia would've probably exorcised Gaou asap. There's no way they didn't hear about him sprouting wings on the battlefield to slaughter their enemies, regardless of what vessel he had, imo. It might be a legitimate power developed from being a Venomania descendant, similar to Germaine's healing ability with Banica.
One thing to note, the narration about the birds looking like they were burning in the night sky might've been an allusion to Kayo's husband. Maybe he used his wings to escape but was still burned and crashed at the mountain, becoming Gakusha?
Considering the reference is coming up again, I'm inclined to believe this isn't just a coincidental legend about the Octos.