Well, I've seen a number of ATI/AMD specific issues through the years, and even did the occasional hack to get applications to work with them, so it's not all that far off to assume they're at fault yet again. ;-)
Not much I actually can do through the SDL API, as it wraps these details - but I wouldn't be surprised if there are workarounds in newer versions of the library. You might want to try replacing the SDL.DLL that comes with the game with the latest one (2.0.12, 32 bit) from here:
https://www.libsdl.org/download-2.0.php