given the choice, he would have chosen to live
How would you know something like that?
This will not be popular, but people who own animals often project their own feelings onto these animals.
I too would feel far to guilty keeping that poor animal alive, for my own enjoyment, while he suffered so much. This is not a feel good story to me.
I don't profess to know what the right thing to do in these situations is, and I am not saying that you are wrong, just that it is not so clear cut as that. Especially if the dog is still having good days (which the essay does not say one way or the other).