My dog would definitely try to take it out but it's the same as with cats: I would be more worried about the old guy losing an eye than hurting the cat. Those rotor blades look pretty dangerous to me.
My cat killed my small RC helicopter, by carefully observing and then jumping at it, and when it was down she kept hitting it until parts came off and I took it away - but for a moment there I was worried that she had hurt herself on the blades. I can't imagine Prime Air won't have some kind of shielding in place.
If she has kittens I would like one.
I think the original author wanted to imply, that a more productive discussion would occur if we'd think of how to fix these issues. Like put a protective cover at the rim and a grid at the intake so air can flow, but hands, eyes and paws are safe?
The rotors can be made safe enough. It is more a question of the damage it can do by falling out of the air or causing some other accident.
Maybe they could do something like the Spirit and Opportunity rover's balloon mechanism to make it safer in case of accident. It would still be heavy, but it wouldn't be hard and it would have much greater air resistance so it would fall slower. Or maybe they could have helium canisters that inflate a balloon big enough to offset a portion of their weight. It'll probably be difficult but it seems like there are a lot of possibilities to explore.
Stop worrying.
Maybe worry for all of them. I would. If I had a dog.