Again, not sure why that happens. The reason there are 2 different messages, depending on whether or not you are in full-screen mode or not, is that IE prevents code from having too much control. This is most likely based on out-of-control scripts and web sites that do bad things. Much like how pop-up blockers prevent pop-ups from occurring unless they are a direct result of the user initiating them.
When you are in full-screen mode, you don't get a standard windows close button (because you don't see the standard windows "chrome" - that's the title bar and edge around the window). So the close button (X) that you see in the upper-right corner is actually a button that the TD puts there. When you click that close button, or the "Exit" button on the Game tab, you're basically telling the TD that you want to exit, and it is able to react appropriately.
In window mode, when you click the standard windows close button, IE informs the TD that you've pressed that button, but does NOT allow the TD to decide whether or not to actually exit - it leaves the choice to the user. So, the TD does the most appropriate thing - asks the user to save the tournament if changes have occurred, and then tells IE to NOT exit immediately, but give the user the option. That's the "Are you sure you want to navigate away from this page?" message. At this point, it's all Internet Explorer - the TD has no control. If you press OK, it should exit. If you press Cancel, IE should NOT exit. But regardless, it is out of the TD's hands.