I dunno what Atheistic satanism is, seems like an oxymoron to me.
Satanism is a diety, and atheism means you don't believe in a diety. So it's satanism without satam
"It is the position of The Satanic Temple that religion can, and should, be divorced from superstition. As such, we do not promote a belief in a personal Satan. To embrace the name Satan is to embrace rational inquiry removed from supernaturalism and archaic tradition-based superstitions. The Satanist should actively work to hone critical thinking and exercise reasonable agnosticism in all things. Our beliefs must be malleable to the best current scientific understandings of the material world — never the reverse."
(Source: The Satanic Temple-FAQ's)
In atheistic Satanism (Such as TST Satanism), Satan is used as a symbol, not an actual deity.