[Problem Description] The Minecraft “Bad Video Card Drivers” Crash could be frustrating since it stops you from playing Minecraft.
And before you could get this problem solved, there is nothing you could do to the game.
In my case, I have a XFX Radeon HD 6870 played it in LOW and there were a few green texture corruptions in some player's faces, but it was playable despite that.
These steps are now added below the original tutorial.
EDIT (September 19th, 2016): In order to avoid the hassle of having to switch between drivers just to play FIFA 17 Demo, I installed my old Windows 8.1 Pro in a partition (35~50 GB must be enough if you only use it to play the demo).
At first we thought we were done because the game wouldn't run even with the downgraded drivers, but then we found out the game was complaining because it wanted a driver version higher than 16.3 (same issue we had with Battlefield 1 Beta).
By modifying the registry key for the driver version, we managed to make it work!