First of all, if this man sincerely believes that all theists are mentally ill then why is he being so cross? Mental illness is nothing to be ashamed of and I have never heard anyone be so angry about anyone else who suffers from it. Usually we are sympathetic to such people. I don't think it communicates very much compassion if you shout at and condemn them. Maybe he doesn't think they are ill after all. Maybe he just disagrees with their beliefs but is calling them mentally ill to insult them. I think it is pretty cruel to use mental illness as an insult.
But secondly, and more substantially, in what kind of a world can such a thing as mental illness exist? Mental illness is a serious disorder in a person's thinking – they don't think the way they are supposed to think – something is wrong. But that presumes there is a right way to think. However, if the atheist is correct, then our thoughts are something we have no control over. According to the consistent atheist, thoughts are the product of the brain, and the brain is a physical organ that acts according to the laws of physics and chemistry with no input from any intelligence. This means you aren’t responsible for your thoughts – they are just the deterministic results of chemical reactions – the outcome of mindless processes produced by blind physical forces. This means there is no “right” way to think.
On an atheistic view of the world, the brain is a product of a mindless process that has no goal or purpose. There's not a thing called “evolution” that foresaw sentient beings and oversaw their development. There were only physical things acting according to physical law. The brain was not “designed” to think “true” thoughts. It just is what it is and does what it does. If atheism is true, then your brain is not “supposed” to do anything, and the Christian is no more mentally ill than the atheist. Our brains are just doing exactly what the collection of molecules that form them do in these conditions.
To talk about mental illness is to presume there is a right way your mind is supposed to function. That entails a purposer, a designer. So, to say believing in God is a mental illness is to saw off the branch you are sitting on. There can only be a disorder in one’s thinking if there is a right way to think. There can only be a right way to think if we are created for a purpose and are not mere physical beings dictated to by physical law. So, the atheist can only be right if he is wrong! The believer in God can only be mentally ill if ... God exists.