Is it known if in Overlord the action is set in a "real world" or in a "game world"?
Yes, it is mentioned in the light novels.

Spoiler alert for those who only read the Manga and/or watch the Anime:


  It's strongly indicated that it is indeed a real world and that this isn't the first time. There are characters who know of these Players and know how mighty they can be. One example is Evileye from the all-female adamantium group Blue Rose. She is actually Landfall from the Thirteen Heroes who defeated the demon gods, who are indicated to have been players like Ainz.