Generally speaking poor internet connection is just gonna disconnect you from the game not crash and BSOD your system. Odds are if it's directx errors it IS somehow connected to the GPU. Could be bad settings, maybe an unstable OC, drivers arent just happy, etc etc. Keep in mind it was a beta and this kind of stuff was to be expected for some fringe case players.
I'd recommend posting your dxdiag.txt file here that way anyone here can get a BIT more hard info as to what could be goin on. If you havent done one of those before its pretty easy just search "dxdiag" in the start menu, and itll then run a program to compile all the parts and stats, and then you can hit "save all information" which makes the .txt file that you can save wherever.
