Your logic is flawed because it makes an unsupported assertion where an assumption should go (saying “A god is…” rather than “If a god is…”) and it wrongly implies that a word can only have a single meaning, regardless of intent or context.
You're arguing this from an atheist perspective and it's warping your ability to consider facts. You are the one limiting the word to having a single meaning. You think a god has to be God or is just an imitation of the God.
That’s just dishonest spin. Do you truly believe anyone who has said “Gods don’t exist” were claiming the concept of gods doesn’t exist?
No, not at all.
Obviously the concepts exist but the denial is that the concepts reflect real beings as people describe and believe they do. By that argument, you couldn’t ever say anything doesn’t exist!
Nonsense. Gods can be anything, including anyone or anything that does or doesn't exist. You are arguing that a God has to be supernatural creator of the universe and that's nonsense.
So if I say “Eric Clapton is a vampire”, “Eric Clapton is an even prime number” and “Eric Clapton is cure for cancer”, anyone statement that those things don’t exist, made at any time and in any context, is automatically false? What is I say “Eric Clapton is a true statement that gods don’t exist”?
Nonsense. Eric Clapton isn't a prime number, isn't a cure for cancer, is a god and does exist. Therefore at least one god exists. The statement that there are no gods is nonsensical.
I can in context. If I say “No supernatural or omniscient god actually exists in the universe” then that’s exactly what I mean.
And that's perfectly fine. A complete and accurate opinion. But to say a god has to be supernatural or omniscient is false. To so there are no gods is false. To say "To me, there are no gods" is fine.
I might use lazy or unspecific language and only actually say “No gods exist” but actually mean the more specific longer statement. You can call the statement unclear or misleading but you can’t simple state I’m wrong based on a misunderstanding of my meaning, especially if it should be clear from context and common-usage.
Which it wouldn't be or else you wouldn't be wrong. You can say that "No gods exist" and mean that there are no unicorns in Tanzania, but that would be true but pointless and misleading. When you say "No gods exist" that means you are saying that no one no where at any time has ever said that a thing or person, whether existing or not, was ever venerated or attributed a might greater than his / her own and that is false. By definition and common use.
The most common use of the word God may specifically refer to a single God but that doesn't negate the existence, including the actual physical existence, of many other gods and goddesses. But that is what you are suggesting. Insisting upon, in fact, out of ignorance of not only the modern day common usage, but the historical usage as presented in the Bible, Hinduism, Judaism, Christianity, Shintoism, and countless other religious and political paradigms of the last 6,000 years.