I found a temporary fix for this, but if anyone has a real answer to the problem, I will select it as answer.
World of Warcraft
I found that changing the game resolution settings either in game or by the configuration file don't actually change the game resolution but my desktop resolution. The result is that most of the game interface is now off screen beyond my reach.
If I erase the set resolution line of the configuration file, the game by default goes to my desktop resolution. This is where the solution I found lies. Before starting the game, change your desktop resolution. When the game runs in full screen mode, it will match the desktop resolution.
This seems like a round-a-bout solution. I found no one with the same problem on wine or on blizzard's forums (on their forums its always "we don't support linux so we wont acknowledge your question. Please stop mentioning wine, buy Windows"). This is why I'm inclined to believe that there is either another solution.
I thought the solution for all newer blizzard games would be the same due to the similarities in the bug. However, the configuration of Starcraft II is a bit different. Instead of removing the height and width settings on the variables.txt file in your Starcraft 2, edit them to match your desktop resolution exactly. If it is off by one pixel, it will bug. It's possible that no one really wants to run these new games on old computers that can't handle full HD as well. That would explain why no one else has complained about this problem. I can navigate well through the game menus on this machine, but loading a level takes half an hour and once the level starts it runs close to 0 fps (the game quoted it at 0 fps).
Edit: The workaround for Starcraft II no longer works. I have yet to find another way to reset the solution under WINE.