I think it’s just a result of Chinese grammar being a little ambiguous when a verb is used to modify a noun. (Japanese is too, when you think about it, just that using する or される after 雇用 can make things clearer. Even then though, the resultant clarity is just something we get from habitual interpretations based on whether what comes next is more likely to be a subject or an object.) For example, 打的人 (的 being the ‘modification/possession particle’; 打 meaning ‘hit’; and 人 being ‘person’) can mean both ‘the person who hit (someone or something)’ and ‘the person who was hit’. Which it means exactly is made clear by the presence of other elements in the sentence like a subject for 打 or an object for 打.
If I were interpreting these words in Chinese, I would probably assume 雇用者 means ‘employer’, and I would probably use 被雇用者 for ‘employee’, but that’s because 者 is usually used to replace the subject of a particular verb in Chinese and 被 is the passive voice marker, though it doesn’t always need to be used. In Japanese though, 者 is more vague, so when you add that to the innate vagueness of 雇用, it becomes possible to have two meanings.