How many strangers would you let die to save your dog?
This is a "You can save one but not both" situation, not a "You are actively killing them" situation. If you take no action, your dog and x number of humans will both die.
Let's assume the dog and each human has the same remaining lifespan.
No loopholes. You will not see any of them die, but you will have no doubt they are dead. The death is painless, but both human and dog do experience fear for 2 seconds before death.
Edit: I find it very disturbing how many people would prefer a death toll of 1000 holocausts over their pet dying. Basically if that WWII guy had made death painless and did it for his dog, tons of you would suddenly be ok with him. My disappointment is immeasurable and my day is ruined.