The other way you propose of defining religions is so general and vague that it borders on meaningless, and doesn't deal with the fact that different people have different questions, formulated differently, using different assumptions and caring about the answers to different extents.
The OP was just being a little bit provocative while calling those beliefs a religion, which I think can be allowed; at least for the fact that there are a bunch of people that are religiously “atheists”.
even the utmost atheist needs to have beliefs
Only if you equivocate on the definition of "belief" as you seem to be.
> both in the ‘individual facts’ way (you can’t be rational about everything all the time)
Of course you can.
"Everyone has a God (where 'God' means 'favourite thing')"
"Everyone believes in the existence of Hell (where 'hell' means 'being unhappy')"
"Everyone believes in the possibility of "salvation" (where 'salvation' means 'self-improvement')"
Redefining words so that the original sentence is correct is a tad too "charitable", particularly when the new definition is completely at odds with how everyone uses the word.
What if some of these answers are "I don't know"?
Perhaps, but atheism does not answer questions like how the world is created. You can be atheist and believe in big bang or believe that the universe have always existed or something else, or you can just not care. Atheism just eliminates some particular answers like "a god did it".
> Atheism is to religion as being silent is to speaking – and you're essentially claiming it's just another way of speaking.
Another way of saying it is that religions (as we know them) are answers to questions, you can get rid of those answers, disagree with them, etc. but the questions will remain and you will implicitly provide answers to them. Those answers will constitute what your religion is -- albeit one might not examine their answers in any detail.