They are two seperate issues under the umbrella of dogfighting. If they stop dogfighitng they stop having to kill animals in inhumane ways. The killing of the animals is secondary to the actual dogfighting. Killing the animals really isn't even an issue for most, as they aren't seen as anything but a product. The people who engage in dogfighting aren't too concerned with giving a viscious and unstable dog a proper and humane death.
Not all people kill dogs the same way. Some just put a gun to their head, some electocute them, some poison, while others let the dog die in the battle, etc. The humane way would be to perform euthanasia as a vet would, but its not as if these types of people could obtain the necessary materials, have the money or have the sophistication to perform such task. So, when you're in the backwoods without the determined "humane" methods generally, the best way is the most silent way as to avoid being detected.