Generally, animal cruelty can be divided into two categories: neglect and intentional cruelty.
Examples of intentional cruelty include, among others, overt abuse, when an individual purposely inflicts physical harm or injury on an animal ... https://definitions.uslegal.com/a/animal-cruelty
So, if they had succeeded in killing the animal, then no animal cruelty? The cruelty stems from their failure to succeed, but there is no criminality in being stupid. Their intent must weigh in here, it seems, and there apparently was no other motive than to put the dog down.
Drop the charges.