Hello everyone,
So I did some quick testing in regards to this discussed issue and thought I'd update you all on the results of it all..
First and foremost I removed the two .dll-files from the root folder of my project and ran my build in which webgl did not run successfully.
After this experiment I tried reinstalling directx (by using the included dxwebsetup.exe) as well as rebooting my system. This was not a successful operation either.
Lastly, I tried uninstalling directx all together and reinstalling it once again (as well as rebooting my system). This, however, did seem to do the trick as I now require no seperate .dll files in the root of my build folder for the project to run webgl successfully.
Thus, In conclusion, I'm not entirely sure what to make of all this other than directx seems to be a bit iffy when installing? I haven't a clue why it worked this time as compared to the first time I installed it when it did not. I hope this brings some insight on the issue..