I cannot do a search to find out which of the dozens of PEW articles that you-in-particular are referencing.
However the article says, "At the same time, roughly one-in-five self-described atheists (18%) say they do believe in some kind of higher power. "
The beliefs in buddhas, bodhisattvas, honored ancestors, devas, nature spirits, enlightened aliens are obvious non-god higher powers. Not to mention the intentionally purely metaphorical gods, such a Spinoza's God or as in some forms of Wicca.
By claiming that those "atheists [are] in fact theists", you are falsely equating "higher power" with a god.
No. Theist comes from Theos which means divinity.
Also, atheists are generally more educated in religion than Christians. I highly doubt that an atheist would consider the Buddha as a higher power. That, you just assumed for whatever reason.
Devas means Gods. Deva means God. Devathva means Godly. So that's theism. I think you just made up enlightened aliens as "higher powers". Its strange you missed the first part of point 2 but focused on the latter part "Higher Power" to make some alternatives up for arguments sake. Very strange. See, making things up just for the sake of argument is not valid. Rather, study the PEW research and how it was done.
The word Theos does not mean "The God". The God is Ho Theos. The word Theos with out the article is a word that means divinity. Thus, theism means "believing in some divinity". Theos basically means any thing someone thinks is divine. Any power or if you like the word "Higher Power". That is why in the point in which you missed the first part it says that 81% of the atheists fall into the definition of atheism and the rest dont.
Its strange when atheists make arguments like this which comes across as so dogmatic. "No no. My atheists are all like me. Dont say otherwise. I will even argue with some dogmatic, tribalistic argument to save my tribe."
You guys are affirming that you have made a religion out of atheism.