To understand what "God (or Thor) exists" and "God (or Thor) doesn't exist" mean, you need a brain and an act of cognition. Each takes place in a brain and involves natural systems embedded in natural systems (that, conveniently for Harris, are mostly opaque at this point in human history). To take a position on the existence of God is an event, not the absence of an event or a non-event.
If you're a rock, baby, or monkey, nothing happens involving the term God. There's an absence of things happening related to the term God. That's a non-event.
Harris rejects the assertion "God exists." He doesn't admit as much, but he does reject it.
What atheists do lack is the cognitive act of agreeing to the proposition that God exists. If you think that's what atheism is, maybe you're as misguided as Sam Harris. Again, atheists reject God belief. They answer negatively to the "does God exist?" question. They've dedicated considerable brain resources to the question of God. Absence of an affirmative is part of a complex process, and, unlike monkeys' thoughts on God, it exists. And unlike beliefs about Thor, it matters.
So why do New Atheists denaturalize and deobjectify atheism? I'd suggest it's so that it can't be studied and measured against theism. This is, ironically, an intellectual move theists are known for -- remove God from the material world and declare him off limits to scientific investigation.
Now it's really quite simple to naturalize non-God-belief (NGB). I just did, in fact. You simply situate it in the brain, identify it as the brain event it is. It's also very easy to make apples to apples comparisons between atheists and theists. This is as good a time as any to admit my bias -- I believe that atheists exist. The only reason the ontological status of atheists' belief that God doesn't exist is relevant is that so many atheists insist on using it to immunize themselves from scrutiny. Apples to apples, theists to atheists.
Theism versus atheism, on the other hand, is a philosophical question. It deals with unmeasurable abstractions. If it turns out that no harm comes from theism, no 21st century intellectual should have a problem with it. There'd be no good argument for antitheism. But Harris claims that harm comes from theism. Theism versus atheism, the philosophical debate about God's existence, has nothing to say about harm. To answer that question, you study atheists versus theists.
Harris implies that God-belief (GB) causes bad things whereas NGB doesn't cause anything. If he wanted a decent hypothesis, doing away with the absurd "absence of belief" angle and comparing apples to apples, he could suggest that GB causes more of these or those specific bad things than NGB, then compare, for example, atheist and theist levels of violence, and speculate about what causes the difference in violence levels, whether it's really GB or something else and if GB, what about GB it might be. In order to compare violence levels, you'd need to factor out rationalizations for violence (because they near-universally accompany it), which means, contrary to Harris's line of argumentation, that F-16s, napalm, white phosphorous, nuclear weapons, etc. all get filed under "violence" when used, regardless of who uses them, at which point Harris would be (further) exposed as the western secular violence apologist he is.