What do observers do in eSports?

Your third guess is the correct answer.

Observers direct all the camera work that you see on screen during the match. They work in tandem with the casters to provide the view on screen to what the casters are talking about. In large events there are dedicated observers that are experienced in paying attention to the minimap and have a good understanding of the game. At smaller events, the casters sometimes will also do the observing.

Observers highlight key things that are occurring during a match. It can be the big fight is going on in the middle of the map, or a drop going on at the same time. Sometimes, it is something as little as noticing that a player is getting a quick upgrade. They are the cameramen of the game.

Or they could just be talking about the Protoss unit ;)