The point of the statement is really to weed out beings that satisfy the previous requirements and yet had nothing to do with life's existence. A being that purposefully created life on Earth carries the responsibility of its existence, and by extension an authority that another similar being would not carry.
It isn't that I would necessarily worship such a being, as they have to pass all four requirements, but a being lacking such responsibility seems like nothing more than opportunism.
I like the comparison to parents that you use, but I think its more like continuing to love and respect one's parents regardless of their plans for you or your relative adherence to those plans. Parents carry the responsibility of the creation of the child. This responsibility (typically) carries the same type of authority that God must have.
Having been adopted, perhaps I have a slightly different perspective on this than others, especially since my birth parents are alcoholic drug addicts who wanted nothing to do with the poor ickle sick child with prenatal alcohol and cocaine exposures. But, being myself, I can't help but come from my experience.
Creation is (sometimes) quite nice. However, it is hardly the be all and end all. In deism, a god creates and goes away, like abandoning a baby on a doorstep. It cedes the responsibility.
If another 'god' or preternatural power or whatever, comes along and actually takes the responsibility over, akin to 'adopting' the creation, and doing all the work, why would it be right or even just logical to not consider it a 'god,' solely because it did not create the life, if it did everything else for it?
To go back to my comparison of parents, if "God" does the creation and "Preternatural Being" (who has all the same qualities/abilities, but did not create) did all the heavy lifting, the caring for, etc and then when the work is done "God" shows up again and wants offerings and sacrifices and worship for doing nothing, why is it more of a god than the "Preternatural Being"?
I feel like this is edging into philosophy a little. I don't know whether to be amused or apologise.