I doubt whether the puppy's death was the result of oxygen deprivation, which I agree is unlikely, but separation anxiety, terror and stress probably caused heart failure, poor little chap.
From CBS: Retired airline captain Denny Kelly says the pitch-black overhead bin is dangerous for any live animal.
"There is no circulation at all in there," Kelly said. "They're scared, their heart rate goes up and they use more oxygen. And there's not enough oxygen in the first place, that just makes it worse."