You seem a bit mistaken.
疫病神は、神という名前が付いているが、信仰を求めたりしない。普通の神様ではなく、妖怪の一部である。
Although Jinxes (yakubyougami, "plague god") have the name "god" attached to them, they do not seek faith. They aren't your average gods, they're a type of youkai.
(...Despite it saying she's also a curse god. She might as well be either.)
She isn't a god per se, but she could be construed as a god (basically a god, or youkai, of nagashibina). The thing is, even if she would originate as a god, because she amasses misfortune and it negatively affects the people around her, she becomes a taboo, regardless of her intentions. Because of this, she would turn into a youkai, and her existence would rather become dependent on the misfortune she gathers. Or something.