I'm thinking it was just content that didn't make the cut.
This. I've been looking at the Windhelm Pit worldspace, and I now think that this arena was the original prison system for Eastmarch Hold, as it is located
exactly where the current jail is. It would be interesting to see if it would be possible to add this arena back into the game world. Things like the current jail would have to be moved a bit, collisions would likely have to be built, and additional scripts and dialogue would likely need to be created, but it could be possible.
Update: I've been studying the Bloodworks (I've been wondering why it was called that), and I discovered something. At the far end of the hallway, just past the stairs that lead down to the holding cells, is an inaccessible piece of hallway behind a wall, which I'm certain once led into the spectator area of the "Pit." It is also entirely possible that the original entrance into the combatant area was originally located in front of you as you enter the Bloodworks. This seems fairly consistent with the overall layout for the arena. I am personally tempted into putting the doors back into the Bloodworks, linking those doors to the ones in the arena, and seeing what happens if I try entering this awesome-looking place.
Update 2: Okay, I did it! I rebuilt the hallways I think once led out into the arena, added the doors in the Bloodworks, and linked them to the doors in the arena worldspace. Now, there seems to be a few missing textures and a single pedestal on the right side of the door on the spectator level that is missing collision, but other than that it looks pretty complete, and by just having this area accessible, it definitely adds a lot more character to the current prison, and makes the design of the prison make more sense. If Bethesda decides not to go back and reintegrate this arena into the game, then it would make a great mod project. Either way, it would be a mistake for this to never see the light of day again. Also, I was right about this being part of the original prison system of Eastmarch Hold. I'm assuming that the holding cell lacking the door would've been where the player would spawn after being arrested, and then the player would then have to fight for freedom.