That's irrelevant, he didn't have to. Harsh conditions together with the aftereffects of polonium and lousy healthcare were sure to do it.
Putin was obviously behind poisoning him first, and putting him in jail second, that he MAYBE didn't order him killed a third time is completely irrelevant, since we know he definitely ordered him neutralized at least twice.
Putin is a mass murderer, and that's even without counting the wars.