Theism isn't an incredibly general term. It means, the belief in a deity. The dictionary definition seems to be more strict; whatever, we can use the broad definition. The definition itself, is specific. One has to actually believe in a deity. One is not a theist, if one does not actually believe in a deity.
Atheism, the way you are proposing it, would mean not only a disbelief in deity, buck also, an ambivalent or even non-knowledge of, the concept of deity. You are proposing a definition that is not only //more than one meaning//, but one that does not have an implicit meaning when written alone. We call words like that ''meaningless''.