Thanks. (Part of the reason this confused me so much is that, in the story, the only person who could plausibly perform the 遊んで action is the same person who is wanting, but of course you had no way of knowing that.)
[A person]に遊んでほしかった is often used in a context [a person]に私と遊んでほしかった. In this case, the person who is wanting is the same as the doer of 遊ぶ as a result.
[A person]に遊んでほしかった is often used in a context [a person]に私と遊んでほしかった. In this case, the person who is wanting is the same as the doer of 遊ぶ as a result.