I would agree with variant, in that I would hypothesize, in many situations, the person that they are trying to convince so strongly is
themselves.
On the other hand, forums like this may exist for the purposes of non-believers to observe the behaviour of religionists that are having their beliefs challenged. An entertaining idea.
Popcorn, anyone?
Idk. In my experience with many believers who seem thoroughly convinced that their specific system is the safe bet, the right path to truth, etc ... I think they are beyond the point of using non-believers as soundboards to, unbeknownst to them consciously, convince their own selves. I would surmise that many of them view the unbeliever as a challenge, a chance to earn brownie points so to speak, a chance to do something in the name of their system (i.e. witness, evangelize, befriend, etc.) If there is success, then they can count it as a win for God. If there isn't, then at least they tried their best, or perhaps they may even view it as taking a stand for the cause, perhaps even a form of persecution, "warfare", etc. IOW, I believe many view it as a duty and a chance to serve.
I think there is a common belief, imo, that, "The atheist knows they are wrong, they are just in denial of what they already know to be true." So an angle is sought: emotional, mental, spiritual, etc, to appeal to what they may believe is already there and get you to face it. Manipulate the atheist into seeing the truth. Or, if that doesn't work, use the atheist to reaffirm their own standing and the atheists demise. It's a win-win. But honestly, and maybe I'm biased form personal experience, I think the idea that many of them are just projecting in order to truly convince themselves ... I don't think that's the majority. My two cents.
To clarify: I'm generalizing but in the context of those who do engage atheists and unbelievers with certain motives of, "How can I reach this person ?" or similar variations in mind. I realize fully that not all believers are the same, etc and so forth. Yes of course there are those who do not feel or believe anything along the lines of what I stated above, etc.