"FFXIV Has Stopped Working"

[Syx]

This is true, but the kernel does not access all of the RAM all of the time. There could be addresses in RAM allocated towards programs that would not get touched by sensitive operating system processes. If there is a phsyical defect in the user mode RAM, it wouldn't reflect as a BSOD to the kernel, since the address is outside of its protected allocations and in the USER MODE physical address range. You can use http://www.winsiderss.com/tools/meminfo/meminfo.htm to see how the RAM is physically divided by Windows on your system. You can then go to the Device Manager, go to view, and Resources by Connection and view what hardware is occupying what physical address ranges. RAM usage is much more complex than what you suggest, which is why I suggest testing your hardware first. It's easier to do than debugging software, especially for users who aren't computer savvy. The only way a BSOD would occur from hardware problem in RAM in User Mode is if it was calling a driver that was buggy, like a graphics driver. WDDM lets part of the graphics driver processes exist in User Mode, but if the problem was part of the graphics drivers, you would likely see errors in other games.

After you rule out your hardware, start auditing your programs. Go through your Programs and Features and remove any unused and/or unknown programs.