Jigsaw is a murderer no matter what he claims.
Let's think about this.
He thinks that he is not a murderer because his tools and contraptions do the killing while he provides the victims with a means of escape. But in the end, if the victim dies they died at the hands of Jigsaw's contraptions in which he put on the victim against their will. This is murder regardless.
Let's use a similar scenario.
You have a friend who talks about how much he hates his life. To teach him a lesson, you hit him with your car then while he's injured and dying on the ground, you give him a cellphone to call an ambulance to prove that he would rather live then die. If your friend is unable to crawl to the cellphone or refuses to call the ambulance, YOU are still considered the murderer.
Just because you give them a way out, doesn't clear you of the fact that you premeditated that act to put your victim's life in danger intentionally.