"Atheism" is a supercategory like "religion" so it wouldn't make sense to try to find specific ideoligious beliefs for "atheism" and more than it would for "religion".
However, within the vast category of 'atheists' there are many real ideoligions.
They're fuzzier on the edges than traditional religions because they're not formalized this way (usually). But if you just look they're not hard to see.
Nationalists from America or China or many other places, LGBTQ activists and social justice warriors, communists of various stripes, radical feminists, men's rights activists, transhumanists (in the Ray Kurzweil sense), rationalists (as in the rationalsphere), environmentalists and eco-fascists all exist. Individuals mix them together to fill the hole of meaning left by religion.
In these belief structures you can always find some story about the moral structure of the universe, and generally a prophecy for the future. You can always find the rituals, symbols, shibboleths. You can always find the community-building practices, the ingroup and outgroup boundaries. You can always find the moral gradient; the definitions of good and evil which humans need to make choices in the world.
There's a reason the moral guide is called that and not 'priest'. Protest or activist leaders, commissars, authors, professors, judges, speakers can all function as moral guides.
Pride parades, military parades, protests, book burnings, national festivals, conferences, dances in the desert, and drum circles on the beach all serve the social function of rituals.
Atheism that believes in moral realism (which the vast majority do implicitly) isn't that far from formal religion, really. (The idea that it ever was was always a Western Abrahamic thing anyway. Buddhists, Confucianists and others have always been basically atheist. And even beliefs like Hinduism or Shinto don't revolve around a god telling people what to do like the Abrahamic religions do.)
The universalism of *belief* was one of the ideas that I was happy to explore and communicate in ideology. I find it interesting to think about. And I think it's important to be able to map these functions from one belief system to another and understand the deeper psychosocial needs these beliefs fulfill, and how they all fulfill them one way or another.
Unfortunately game mechanics, being rules executed by a computer, must necessarily be formalized in a way that real rituals and moral guide positions don't. I did my best but obviously that forced formalization loses a lot of what's being simulated. Gameplay, clarity, and being able to actually build the thing in a non-insane timeframe always took precedence. Still, the idea is there and give how hard it is to express ideas in game systems I'm pretty happy it made it through the development process.