I'm in a very secular country. Non-religious people are... non-religious. I don't believe there is anything that "replaces" religion in most people's lives. If you're not religious, you don't necessarily have metaphysical needs, and I think most people here don't.
Regarding religious people: they meet with eachother in church and other constellations as usual. Nothing is keeping people from practicing their religion, but they can't assume most people will empathize with their views, which is true for many different standpoints in life, not just religion.
(I did not read the article as I was paywalled, I might have missed the context of your comment)
There is ritual around death and marriage. The scene of a temples will be typically older people eliciting prayers for health, relieving ailments.
But little else that I have observed.
It is perhaps the rest of the rigidity of their society that gives them a sense of belonging to, serving the whole, a notion of laws, rules, guidelines....
So faith is, religion is not.
Perhaps organized religion was serving to keep people's need to be part of something more productively contained. However I can tell you it isn't universally a neurological need. There are those of us who get by just fine without any religiosity, or church. I don't know if that is because we are different or if anyone can do it.