What is the ruling on someone who intended to pray the 'Isha prayer, believing it to be so, then it became clear to him that it was the Maghrib prayer? Should he complete his prayer with the intention of Maghrib, or is he required to repeat the prayer anew?

You must intend the specific prayer. So, if you intended 'Isha' while it was Maghrib, the prayer is not counted. You should have interrupted the prayer immediately upon realizing the mistake and started with the intention of Maghrib. However, since you completed it and performed the missed rak'ah, your prayer is valid, and nothing further is required of you.