When you bring a pet into your household you're responsible for taking care of it
, it's grossly immoral to hurt it simply for fun or to selfishly relieve your own stress. Comparing a pet to livestock or vermin just doesn't jive. Like you might put down poison to kill a rat that you found in your pantry cupboard, but if you poisoned a rat that you had brought home from a pet store, fed, and trained to trust you, people would justifiably think that was horrible.
At least the gf/her daughter in OP's story sound like they had a normal response, hopefully they'll be the ones to take the cat in for treatment if it's still alive.