Check your graphics drivers are up to date. That is DirectX struggling to open, which could possibly indicate that it is corrupted or non-existant.
Check here for more info. https://support.steampowered.com/kb_article.php?p_faqid=772
I'd also go to Windows update and check your system is completely up to date. Else: https://support.microsoft.com/kb/179113?wa=wsignin1.0
dxgkrnl belongs to directX. I'd start by making sure you have the latest version of direct X and reinstalling your graphics drivers.
Ntoskrnl and dxgkrnl are both core windows drivers though. If you keep crashing after updating/reinstalling graphics drivers, it's time to start looking for hardware issues. RAM and HDD are the most likely culprits. I'd run Memtest, which you can find under "tools" at the top of the page, and whatever flavor of HDD diag you prefer- I like Western Digital's Data Lifeguard.
what happens when you run dxdiag? This will tell you about your DirectX version and your hardware. Make sure the hardware setup matches what you think you have. You can always un-install it and download the latest version from Microsoft
Also, this is the price you pay when you build your own computer. You got to know something about it. Dell or some similar company are more than happy to provide a computer they guarantee to work out of the box. Just like an Apple Mac (and way cheaper). Some companies, like Best Buy, will also provide support, similar to the Apple store.
In that case, we will need as much information as possible to narrow it down: operating system, GPU model and driver version, screenshots of the game's folders, a list of running processes and the content of the log.txt file in the game's directory would be a start. Also, what method was used to install SweetFX?
A quick Google search seems to indicate SweetFX having problems with Windows 8.1 and DX11 games, yet it should apply to GW2.
In the meantime, it never hurts to manually update DirectX (9.0 // more). That solved issues I had with GW2 + SweetFX in Win7 64bit.
DirectX https://support.microsoft.com/kb/179113/
And it depends if you have AMD or Nvidia card
AMD: http://support.amd.com/en-us/download
Nvidia: http://www.nvidia.com/Download/index.aspx?lang=en-us
The Web Installer will install the latest version of each individual d3dx library. An app shouldn't have a dependency on a particular version of an individual d3dx library (i.e. don't need a specific version of the DLL with the same name). The point of the Web Installer is so you don't have to manage all the different versions.
I was looking up information on DirectX this morning, and this article, under the section "List of file failures that the DirectX End-User Runtime package fixes", lists the files it will install. If a program needs one of the files listed, it will be installed after running the Web Installer. If the program complains about the wrong version, the program's doing something wrong.