Ok. I am now referring to the ASUS website and I am downloading their most recent recommended driver for my computer (it's likely the one I had already been trying to download from other sources).
I just installed the recommended ASUS driver from a zip folder. I'm about to reboot my computer. However, I am seeing that the recommended driver from ASUS is labelled 10.18.10.3308.02. That might be the very same driver that was giving me BSoDs. But I am going to play league of legends soon, thus I will see then.
I will immediately come back here with information on what has happened.