I think you're making Steve feel bad, and he doesn't deserve it. The joke was not intended to make anyone feel foolish. It's humor comes from the unexpected punchline, the unexpected interactive way it was delivered, and the unexpected application of the common phrase "run out of gas." There's no way to write this joke without the part about the dog maybe dying.
It's very hard to judge whether a joke will offend someone, and if you worry too much about it, a lot of funny things will never be said. Steve saw that joke somewhere, and thought people would enjoy it here. I'm sure he didn't think "Hey, they'll feel really bad at first and then foolish." He wasn't making fun of sick dogs.