Well, I don't know. I'm an atheist. So, if I answered my own question, since I've never known of a god the closest definition I can get (from others) is an experience or a source of spiritual awakening. At times I think it could be something believers personified. Other times when they say he did this or that, it makes me think of mythological gods especially in scripture in how its written and what the concept of the christian god has done.
So, as an atheist, the closest description I have (therefore ability to discuss it) is the christian god insofar my definition being either an experience or a mythological being. Though, I side for the former only because most people I talk to who believe in god experience him not hear him in an audible voice or see him dance in the stars (or how some say, be pink unicorn or spaghetti monster).
Another example on the opposite side would be if I asked the christian the same thing, his or her concept of god is, well, jesus christ. Jesus christ was human so it's easier for me to give a definition of that particular "god" because I have interacted with humans before.
I do feel the question is logical-how can you, say, blame someone that doesn't exist-but many people have christian upbringing and in my opinion using the god as a scapegoat for how they feel about believers claims of god. However, to ask about god itself, I'm sure they have some sort of concept or they wouldn't be (or couldnt) talk about it.
Trying to find a consistent definition for God feels pretty futile. Even among Christians. So I try as best I can to ask the "believer" to define their God. So IMO, how a believer defines God is really a reflection on them.
I suppose what you are saying though is some atheists use their own (the atheist's) personal definition to attack the position of the believer. Maybe, I think sometimes that this "personal" definition for God came from other believers.
Many Christians feel they have among themselves a consistent definition of the God they believe in. They don't. However, an atheist may find themselves getting caught up in that assumption and using what has been defined by other Christians to attack a claim.
So IMO, God is a fiction created by our subconscious mind. The subconscious mind files away all the information about God, religion, what we hear, what we see and uses it to create and God for us using our feelings and to a degree our senses to support the existence of this God.
While there is some commonality about the information we received the rest, what we see what we hear what we read is unique to us. So while some similarities exist, the God each individual experiences is unique.
If you want a definition of God, there exists as many definitions of God as there are minds available to consider such a definition.
For God to prove they exist they would need to prove they are more than a fiction created by the subconscious mind.
Considering how many definitions for God exist, this is not looking good.