Mea culpa. I think I've fixed it.
Do you mean that an entity becomes a God solely for the reason that someone chooses to worship it, that it's something humans can bestow? That there is no independent quality of 'godness'?
A 'false god', can be be worshipped in the context, of that false god, having 'godlike qualities'. The usage of the word, god, there, directly infers this, as well, because the same word is the name, or one of the names, of the Real God. Using the same word, correlates to the fact that the false god may very well, have godlike qualities, the false god may have qualities that are similar, to the Real God.
The nature of God, and false gods, is independent, from human classification. The classification occurs as a result of the belief in those qualities.
I'm not concerned with revelation ─ if God is real then God has objective existence and therefore God, like any other real thing, can be looked at directly or via suitable instruments. To design those instruments we ask those who hold that God is real what God is; and when they tell us, we know what we're looking for. If they don't know then neither do the searchers, and no one knows what they're talking about.
I disagree with that premise. We can know what we're looking for, however, note that this is subjective. If one wants to worship demons, for example, as gods, they will simply give the title of god, and the god they want to worship, to the demon.
That can't be said of imaginary gods, where the situation is much clearer ─ they can be anything anyone wants.
Believers do not consider God to be imaginary. Hence, the attributes of God, are noted, so forth. Thusly, the Bible, and extra Biblical texts, and what we know of God.
Note: to clarify, humans do not have the 'godlike powers', that some demons might posess to varying degrees. Of course humans are actually at a higher level than demons.