is this a logical fallacy existence is proof of existence

Atheism is a lack of religious faith. Really, that’s how it’s used by the vast majority of people who self-describe as atheists, and saying it means anything else is rather presumptuous. It’s also a classic insult: “You’re an atheist! That means you hate God! You’re just as faith-driven as me, but you’re hateful and smelly!” So be careful when you try to define it for people, even if you can dig up a dictionary which supports you. Remember: Dictionaries once defined homosexuality as a mental illness.

So it isn’t fully symmetrical with theism, and it isn’t even about lack of faith in the existence of a deity. It’s just that for thousands of years, Western religions have been defined by their belief in one or more deities apiece, and given that we’re all speaking English here that Western assumption is common among us.