Without getting into details, I'd just recommend checking out this tvtropes link on villain protagonists. I think you'll find it hard to disagree. He embodies all the characteristics of a villain, and at best is typified as a sociopathic hero who crosses the line into full villain upon killing Marlene.
I would say that at the hospital he wasn't at his best mental state and he also knew that if anyone was left alive that knew about Ellie she was going to be hunt. And sure after all the kill he done in the past he wouldn't have issue killing a few more.
Anyway even criminals have loved ones and can act kind. And he being able to sympatize and have real care and love eliminates him being a sociopath.
duduspace11 "Well, since we are estimating costs, Pokemon Red/Blue did cost Nintendo about $50m to make back in 1996"
Mr Puggsly: "Hehe, I said good profit. You said big profit. Frankly, not losing money is what I meant by good. Don't get hung up on semantics"
Azzanation: "PS5 wouldn't sold out at launch without scalpers."