Without reading beyond the OP's quotes (when starting this post, turns out the article is the same afterwards), a type of module evolved to quickly infer relations about the world or decrease stress at uncertainty is certainly a qualifier for an 'instinct' that returns at times of intense stress as well.
It does fit with individual and social observations whereas other models can explain one part but not the other because they pretend it's somehow not a cognitive function that has to obey an evolutionary framework just like any other. There's nothing sensational or new about that proposition.
However, the inflammatory title of this thread doesn't help. What it means is that, like all instincts, it's a shortcut to a certain effect but that also means it's very limited in its flexibility. Human brains are basically either efficient (instincts, etc, 0.2 second response time) or flexible (conscious abilities, 0.5 second response time) and which route gets activated on certain triggers matters a lot. The suggestion here is that religious concepts and associated contexts work similar to an efficient circuit, that is: a quick response is made but it's almost always the same because there's no self-aware processing involved. Habits are all of that nature.
The "smarter" part, as much as I can infer, would relate to the less religion-connected contexts in an atheist brain versus a religious one, meaning that specific triggers, say the value of life or the meaning of love in relationships, do not get the smaller range of 'standard replies' that you get from religious minds, because atheists literally have to (and can) think on it a little. You can probably measure this in the face as well, as thinking would drive the eyebrows down for a moment and a directer instinct would have no such impact, leaving no change in expression (which you've probably noticed a few times already in life when people reply without thinking).
That doesn't mean they're actually (physically) smarter in any way or form, it just means that other circuit paths are triggered and they can use a greater flexibility versus the limited flexibility created by the greater efficiency of (deeply) religious minds / brains.
If you measured stress as 'levels of getting tired' from specific questions, I will wager you right now that an atheist would get tired over time from them because their brains have to expend more energy than a religious brain does, which should also make them less tired since they're basically using half the energy if going only by response times.
Those efficient circuits however, include ancient and more basic ones like violent reactions and so efficiency can bite you in the ass when the wrong path is triggered. A flexible circuit would give you a chance to observe the response and amend it or veto it, like raising a fist and then realizing you probably shouldn't. Applying this on religiosity is just one example that's somewhat easier to demonstrate, that's all.
This is not my field or anything, but I know enough about it, I think, to say I'm not too far of the specifics here.