So . . .
The actual issue seems to be, is morality a function of religious belief?
Is that the essence of the OP question, or is there more to it?
I think that the article author believes something along these lines, though that is not his point in the article (which is more along the line of, "atheists do not have faith or allegiance in something outside themselves and such is a necessary but insufficient requirement to be a good citizen.") Because, in the author's logic, good citizenship implies passing the culture/society on to following generations and atheists do not have the moral framework to explain why our particular culture is good to those that follow or defend it against its detractors.
I think that self-declared atheists can have a moral code (and be good citizens). That comports with what I have experienced. But, IMO, every "atheist good citizen" I have encountered has some faith that can not be supported by logic & reason alone. That belief might be in the founding documents (a secular faith similar to Lincoln's before his presidency), the non-aggression principle, love of liberty for all, fair play, etc. Barring some such faith, my answer in "No, they can not be a good citizen," as they lack the necessary moral sense that will, at times, place the well-being of others above one's own self-interest.
In a large society such as our own, logic, reason, and empiricism show that a purely amoral, self-interested outlook is the one most likely to result in the greatest material success/comfort for the individual. Convicted criminals, those who most obviously display such an outlook, have (on average) below-mean intelligence. IOW, they are not very good at what they do. As a cop buddy of mine (of very high intelligence, himself) says, "We only catch the dumb crooks. The intelligent ones rarely come to our notice beyond the effects of their crime on the rest of us."
The above-average intelligence, self-interested, and amoral person likely will never come to the notice of law enforcement.
The wicked do, indeed, prosper...if they are not idiots and can manage risk. Our political class is full of such bright, amoral folk, though we must not think they are confined to politics. Most of us have seen the smart, amoral climber who is smart enough to genuflect to those that can harm him, but merely uses and discards those who have not such authority.
Actions such as having children, giving a tithe, foregoing occupations or opportunities due to moral qualms will not maximize one's material success. They indicate a sub-optimal course of action for the individual and can not be supported by reason or logic unburdened by faith or morality.
My worry, supported by what has occurred in W Europe, is that the faith such "good citizen" atheists have is not sustainable. Such deracinated faith dies out and the question, "Why is our culture better than any other or worth preserving?" is no longer academic, but pandemic. Such secular faith draws on the capital/tradition/etc. of more comprehensive faith, but does not produce enough to pass down to preserve and grow the culture.