Your link is to a site hosted by andividual scouter. It is not the policy of the organization.
Faith ends up being extremely hard to define
Correct. Which is why the organization does not actually define it. They explicitly state that it is to be defined by the scout and the scout’s family.
I, too, am an atheist, by the usual definition of the term: I believe in no supernatural deities. However, with BSA’s definition, “atheism” is only possible if I believe in nothing whatsoever. Some extreme form of nihilism. With BSA’s definition, I do, indeed, have a “god”: my own consciousness. I do, indeed, have a “religious” creed: logic, rationality, the pursuit of understanding reality. I wouldn’t normally refer to these as “god” or “religion”, but they serve the same purposes for me that gods and religions serve to theists.
and ask if I am eligible
That is not a question they can answer. They charge you with defining your “god”. You are the authority on the subject, not them.
If asked how I fulfill my “duty to God”, I would respond that within my worldview, the concept that BSA refers to as “god” is more commonly described as “consciousness”. I might mention that within my worldview, it is considered “impolite” and “imprecise” to refer to consciousness as “god”, but that I recognize there is no malicious intent behind the BSA usage of the term. If I got any pushback on that, I would remind the inquisitor that my family and I are charged with defining God and religion. I would further remind them that a scout is reverent, and reverent includes tolerance and respect of the beliefs of others.
I would explain that I fulfill my duty by experiencing, learning, teaching. I would describe a memorable experience, what I learned from that experience, and thank the inquisitor for giving me the opportunity to fulfill my “religious” duty by sharing the knowledge I had gleaned.
If I recall correctly, (it’s hard to look at previous messages with this app), you said you could truthfully describe yourself as your own god. Do you exist? If you exist and you can describe yourself as your own god, is it still reasonable to call yourself an atheist?
If you are your own god, what duty do you have to yourself? Are you fulfilling that duty? Are you reverent? If you can answer those questions (and it doesn’t really matter what the answers are), you are eligible to be a scout.