The other class of drug that would obviously be recognized as effective are psychoactives such as alcohol, caffeine, and nicotine.
By contrast I can't imagine how they could judge the efficacy of e.g. blood pressure medications back in those days, even though there are purely herbal treatments like aged garlic that certainly do have an effect.
ETA: This wiki article has a good overview: https://en.wikipedia.org/wiki/List_of_drugs_by_year_of_disco...
Another notable category of ancient drugs is laxatives.
The first synthetic drugs did not begin to appear until around the mid-1800s. In 1832 chloral hydrate was produced, which was the first synthetic sleeping drug, but it wasn't used clinically until 1869.