I accept that that is what it means because the vast majority of what I read on the matter, dictionaries as well, takes this to be the most fundamental aspect of what the position entails.
My justification for holding the position I hold is irrespective of the label that you wish to attach to it. It just happens to be labelled "atheist". Heck, if the label is what you have issue with then feel free to actually argue against what the person's actual position is, not the label. Can you do that?
My worldview is that everything within the universe appears to be material/physical or related thereto, and run through an ordered structure of fundamental laws. You show me one thing that does not fit within this worldview, that requires there to be something else, and you may be on to something. Otherwise you are simply moaning that we don't believe what you are saying and then blaming us for your inability to convince us.
Whether or not theism is belief in the existence of God / belief that God exists, or belief IN God is indeed a side issue. As is the definition of atheism: neither change the actual things that people have faith in, believe in, or don't believe in. Only if you want to ignore what people say and instead argue against what you think their label means does it have relevance.
I do so enjoy reading your straw men.

Please indicate where in this thread anyone has equated religious faith with theism?
Please indicate where in this thread anyone has said that the faith of the theist is faith purely in the existence of God.
If all you intend to do is argue against yourself and not actually listen to what people say, feel free but exclude me from such nonsense as it is an utter wast of time.
Ask a theist whether they believe God to exist or not, and 100% of them will say that they do.
As a theist whether they believe IN God and not 100% will do so.
The vast majority of dictionaries support the definition that theism is the belief that God exists.
Again, deal with it.
No, not all faith is simply faith - I.e. There are differences between faith supported by objective evidence that anyone can see, and faith that is purely subjective.
It is an issue in as much as it is at the core of what the theist also believes, and it is the one and only belief that links all theists. If the theist doesn't actually think about the existence of God because to them it is a given, then so be it, no one is disputing it.
So, can we get back on track, please?
And are you going to respond to the issues I raised previously, which you have already been reminded of once? Or are you going to continue to ignore, and thus avoid any actual fruitful discussion?