@ThePrincessOfTheRFA
I certainly don't think it was meant to offend Muslims. My guess is that it took the names from some of the biggest religions in the world, and used them without having deeper knowledge of the various religions. I would assume Christianity, rather that Judaism, as Christianity is bigger (especially in Korea), though since it is a Korean author, they could be thinking of something like the "Unification Movement" that claims to be Christian, but has very different teachings, as well.
But even from a more technical perspective, I would say that, while Islam, Christianity, and Judaism all claim to worship "the God of Abraham" (and are all sincere in their attempts to do so), that doesn't mean they all worship the same God. Christians claim that Jesus is the God of Abraham, and so teach that those that claim to worship the God of Abraham, but don't worship Jesus, are not worshiping the God of Abraham. Muslims and Jews would say that Jesus is not the God of Abraham, and so teach that those that claim to worship the God of Abraham, but worship Jesus, are not worshiping the God of Abraham.
For an example from the Book of Exodus (chapter 32), while Moses is on the mountain, Aaron crafts a golden calf, and the people worship the calf as "the god that brought them out of Egypt". That golden calf didn't do that. So even if they claimed to be worshiping God, who brought them out of Egypt, they were worshiping a replacement, instead.
I've not heard people claim that Allah is a moon god or something like that, but there may be those that do (and they would be incorrect if they do). I don't think that was what was implied here, though.
A couple notes on the video. More than once (in the 6:15-7:45 range) the person in the video actually states that Christians don't worship the same God as Jews or Muslims (which contradicts your point). Also, whoever wrote the description is unlikely to actual be a religious Jew, as they list Jesus as a "prophet" and Rabbis have told me, personally, that they would never call Jesus a prophet, but would say Jesus was a "good teacher" or "moralistic teacher", but nothing further. This makes it seem like it was an Islamic video, pretending to be Jewish, to differentiate from (and even attack/mock, based on the tone) Christianity, but it could be the person in the video is a Jew, but the writer of the description is a Muslim. (The author of the description also tries to use "Mars" as an example of an English word that is "genderless" and "can't be pluralized", but Mars is named after the Roman god Mars, and thus is a masculine name. In Hebrew, as well, the same word "Elohim" is used, referring to God, and referring to other god
s, in Exodus 20, which contradicts one of the points made in both the description and the video, about proper titles for God being unable to be pluralized, which if the person in the video is of the Jewish faith, he should be familiar enough with the passage to know he was contradicting it.)
Further (in terms of the "more proper way of referring to our Creator"), for Christians, they would accept the New Testament, which uses the Greek "Theos" to talk about God, and thus using the term for "God" in the language of use would not be considered improper, even if it isn't using the Hebrew/Aramaic version of it (and further how "Elohim" and "El Shaddai" can both be different titles, but still refer to the same God to use examples from Hebrew Scriptures that were mentioned in the video), as it is about the God being referred to, rather than the title (though obviously using a title like "Baal" or "Hermes" would be inappropriate, as those are "proper names" of gods from other religions, rather than just descriptors of deity in general, or descriptions of a characteristic of the deity, like your use of "Creator"). This also ties into the fact that multiple people using the same title doesn't mean they are referring to the same God, just as people using different languages/titles can be referring to the same God.
Sorry the post ended up being so long.