Christianity has a very specific hierarchy of supernatural entities. Obviously their deity sits at the top. Below him are many separate ranks of angels, of which Satan is supposedly a member of the top ranking, just below Yahweh himself.
The deities of other religions are counted as fallen angels deceiving humanity, inaccurate attempts to worship the one true god, or simply the delusions of heathen fools.
In this context, Satan is not a deity, the deities of other religions are not
really deities even if their worshipers
think they are, and there is in fact only one actual deity. There's no need for equivocation - followers of false deities only
believe they are worshiping a god.
It
is however essentially an argument via definition - the argument includes as its premise that there is only one deity. The deck is stacked. It's a matter of circular reasoning. "Since there is only one god, all other gods are false and not really gods at all. Since all other gods are not really gods, there is only one god."
I don't think it's very practical or objective to use Christianity's definition of "god," simply because it's only a valid definition for Christians. All non-Abrahamic religions would disagree with them.
Of course, I'm not sure what common definition of a deity could really be agreed on - not one single version is actually based on reality, none are testable to determine accuracy, and so every definition from the Christian one to the Hindu one to the Pastafarian one is equally valid.
I think about all that everyone would agree with is that "gods" always share the following characteristics:
1) their abilities are (or appear) supernatural, vastly exceeding the expected capabilities of any human being. The laws of physics as we know them do not seem to apply in the same way to deities.
2) They are ageless - while some gods apparently die, they do not do so because of old age. Typically the deaths of gods involve violence, especially a world-ending apocalypse
3) gods have some degree of interaction with humanity, especially in the form of human worship
4) gods tend to be the "top of the totem pole" in terms of relative power to other supernatural entities within the same belief system. For example, while a fallen angel being worshipped by humans or even a poltergeist (a ghost capable of moving objects) would qualify under criteria 1-4, they are "less powerful" than the deities of those who typically believe in them, and therefore are not deities themselves. Hierarchy within a pantheon of deities is frequently present, but even the lowest deity is still typically regarded as "more powerful" than any non-deity. There is also no objective method or reasoning to determine relative power and abilities.
That's still pretty loose, but I don't see how to be more specific. Yahweh and all his angels could easily be considered to be an entire pantheon of gods, with Yahweh simply sitting at the top. Or angels could be considered to be fundamentally different than Yahweh (Christians typically use the property of having been created as the determining factor - Yahweh was not created, and he created everything else, and only that which itself was not created is a deity, with everything else a lesser being, etc). There just isn't an objective way to compare supernatural entities, especially across multiple belief systems.
That's why I think the entire argument is rather pointless - it's impossible to make a real determination over whether Christianity is actually monotheistic or polytheistic or not, simply because there is no way to objectively define "deities" that does not either stack the deck such that the Christian god is the only deity by definition, or such that other supernatural entities are not considered "deities" despite no functional difference.
To me, it seems like this is more an argument over whether Superman or Batman would win in a fight - people who like Superman will point out that he's able to punch Batman into a bloody smear with his pinky finger, while people who like Batman will point our that he has access to Kryptonite, always has a plan for everything including a rampaging Superman, and has beaten Superman in comics before. The
fact of the matter is simply that it's impossible to make an objective assessment when comparing
fictional characters - in the case of Batman and Superman, the one who "wins" in a fight is the determination of the authors as needed for the story, and has nothing to do with anything our hypothetical groups of nerds would rage about.
So too with deities. There's nothing objective to base a discussion around, and so you can't really make a determination about what is or is not a deity (and therefore which religions are monotheistic or polytheistic or even atheistic) beyond the stated claims of each religion's followers. Christians say that Yahweh is a deity while Satan is not; ancient Greeks identify Zeus, Aries, Poseidon, etc. all as deities, but exclude the Titans or the Fates or other supernatural entities.
I think a far more interesting conversation would be to question whether modern monotheistic religions have polytheistic roots from an archeological and anthropological standpoint.
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