Sure that’s a valid defintion, albeit a super specific one and it directly exclude all (or almost all) known forms of religion on Earth.
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Which part is directly excluded?
The one where there is not only zero proof of anything of it being real, but also zero (or nearly zero) religious people actually beliving that.
And if we were talking about whether it were real, or whether people believed it in those specific terms, you’d have a point. But since we’re talking about your assertion that major earth religions are “directly excluded” by that definition of “higher beings,” i still fail to see the exclusion.