Even this charitable interpretation doesn't make much sense: The only thing "atheists" have in common is that they have a lack of belief – we have no idea what they actually DO believe (people come with various philosophical persuasions, after all).

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.