So, I was playing the game, when it begins to stutter. The screen goes dark, then my monitor dies out, and my entire computer restarts on its own. Has anyone else run into an issue like this? The last time something like this happened, it was due to a lack of memory, but I switched the graphical settings to low.
System memory shortages generally wont manifest in reboots unless something is wrong. If you are concerned with video memory then the question has to be asked if your card meets the minimum system requirements? Those requirements are for the low settings and if you don't meet those then you can expect some sort of issues.
That said sudden reboots are often a very serious problem of some sort of hardware issue. I may suggest to you to be open to the idea that it may not be the game at all, and that there could be an underlying issue. Thats not a sure bet but it is worth considering. A program can reboot a system but often needs help of some kind.
Games are just about the toughest thing you can toss at a computer, so if you have any hardware issues it may show up first when gaming. For example you could have an insufficient power supply for your system. When the game starts pumping power to your video card that it didn't need websurfing suddenly it runs out of juice and reboots. I am NOT saying this is your problem, but it is one possible scenario. If you wanted to test that scenario try other similarly graphics intensive games and see what they do. If AW does it every time and other games zero, then it get tougher to nail down.