What if the player cannot hurt anyone directly but activates a button that drops an enemy into lava or activates something that shoots an enemy with an arrow?

It doesn't state a specific method that will result in killing, but "achieve goals without killing", so this can mean player or environmental. A fun interpretation could be that if you don't kill anything you accomplish a "hidden" goal, making it an optional gameplay mechanic. An example I can think of would be something like, if you don't kill any enemies in a level/room you gain some health.