A person who subscribes to theism is a theist. A person who subscribes to atheism is an atheist. A person who subscribes to anti-theism is an anti-theist.I think I have misunderstood the term in the same way. To me anti indicates being opposed to/against. Theist is a person.
For me, an "antitheist" seems like -- one who opposes theists (a person whose foundational belief system is that of opposing other people that hold theistic views.)
Otherwise, if it is not based upon opposing another for their views, then I don't see why the term atheist would not apply. I guess Antitheistic Atheist might come across more clearly to me. Either way, it seems as though it is not a belief system that believes anything in particular -- except that another group is wrong.