That it was intentional, doesn´t make it any better.
A mere undefined word isn´t an "entire concept", it isn´t a concept at all.
I could make the same claim about any and all hypothetical forms of physics too. They all suffer from the ability to be "modified at will", and they all represent a *range* of ideas, not one specific idea.

Irrelevant.
Not really. The biases of the individual can often play a role in a 'lack of belief'.
I don´t reject any "concept as a whole", because there isn´t such "a concept as a whole", in the first place. Before I can address a concept and discuss it, I must know it.
Even your 'statement of faith' that there isn't a "concept as a whole" (related to God) is part of your own "biases", and part of your "belief system". The concept as a whole could be summed up as any form of "intelligent creator", natural, supernatural, or otherwise.
That´s why the existence of the universe isn´t in dispute any more than the existence of the President of the USofA.
So we're really just debating the "character" of the universe, not it's existence.

Same deal with the president.
"Prefer"? The more self-suggesting interpretation would be that the vast majority of God concepts have "supernatural" at their core, and that´s why - without being given a particular definition - people assume that this is what a question regarding "God´s" existence is about.
Well, it "could be" a supernatural definition, but that's not a given.
There is no such thing as a "whole concept of God". There are countless different concepts.
That's not really so. I'm going to use the LCDM example as a counter argument to your arguement. There is a "whole concept" of dark matter and a whole concept of a 'big bang', as well as individual definitions of dark matter, and variations on "bang" theories. The "most common" definition of dark matter is based upon a "supernatural" forms of matter too (WIMPS/Axions), but like the God concept, there are "ordinary" definitions of dark matter as well (MACHOS). I have personally chosen to "lack belief" in the entire concept of 'dark matter' however because I see no need for it in the first place. I reject each specific definition of dark matter for exactly the same reason too, specifically due to a lack of evidence. I also reject all big bang theories, not just one of them because I prefer a "tired light" solution to the observation of photon redshift over distance. I reject the "whole concept" of "space expansion", not just "some" of them.
The way you approach this topic, you are inviting confusion as to whether a disagreement is of epistemological or semantic nature.
The topic itself invites confusion. You can't blame me for that.

Sure I used an open ended question, but that was done intentionally. I know you may not like the fact I did so, but I intentionally wanted to *not* focus on a 'specific' definition, but rather I wanted to understand why individuals atheists lacked belief in the whole concept. Some atheists noted that they could not and would not do that, and required a better "definition". So be it. That's a legitimate answer too.
And I was telling you that the way you did it was a poor approach. (GIGO)
If I were trying to be specific, yes it would be a poor approach, much like if I asked why someone lacks belief in 'dark matter' might be a poor approach. If I wanted to be specific I would have to ask them if they "lacked belief in SUSY theories", or "WIMPS", or "Axions", or MACHOS. I didn't care if they lacked belief in specific definitions of the term God, because I do too! I was asking them to explain why they lacked belief in the concept as a whole.
Many atheists noted that they needed specific definitions to reject the term, while other atheists explained why they rejected supernatural definitions. It was all good from my perspective, and I wasn't trying to suggest that there was a right or wrong answer. It was a good approach from my perspective, even if you didn't see it that way.