Of course, what you've said is true as far as it goes. But, consider this: if your employer has a product with any sort of search capability, your hobby/side project search engine then falls under the heading of things "relat(ing)... to the employer's business."

If you work for a big enough tech company, like, say, Google or Facebook, it's likely that a lot of things will "relate...to their business." And, note, too, that there's no requirement that you actually know that it relates to a part of your employer's business.