One of the core beliefs of Communism is atheism.
I think you answer the question well in post 20.
The world over the centuries has seen millions exterminated in the name of communism, nazism and yes, manifest destiny. Each of these motives were based on a political or social philosophy that rationalized the murder of millions to achieve a certain goal.
More likely, the common thread is the lack of lack of democratic structure in each of the mass killings mentioned. Since, communism lacks such a structure, it makes it easier for a leader to take such action and the people without any democratic power must take the brunt of the wrath or simply watch and hope they are not next.
Thus, it would be much easier for China to send people to death camps than it would be the US or a European democracy. The present day examples would be Sudan and Rwanda where hundreds of thousands have been killed. Not atheists, but mass murder.
[Did Stalin and the others kill specifically for the sake of Atheism? Or did they do so for political purposes? It’s important to make a distinction.]
If men do not beleive they are accountable for their sin, they will break every commandment of God in their lust for power and greed and will eventually stand before the Lord God Christ Jesus in the day of their judgement.
This is why I cling to the cross, that I may be forgiven all my sin against God and His only begotten son, Jesus of Nazareth.
Actually the relationship would come from them having no moral code except their own compass to live on... of which many of these leaders failed.