You can't see me click in the GSX config window, but you get the idea. Please do not gigve me the answer that it works for you. You can clearly see it does not for me, all of the runtimes that are required by GSX are installed.
Of course I'll give you the answer that it works for me, because that's a clear indication the problem is NOT GSX.
Looking at your video, I can see there's ANOTHER application that is interfering, that green line that says "Entering Slew Mode - recalculating data..." which appears very briefly when you Enter Slew and appears again when you Exit Slew is NOT coming from GSX!
I don't know what that is but, depending how it's made, it seems to have intercepted the Enter/Exit in Slew mode and, I can see the Exit interception might cause issue, since GSX needs to know when you Exit Slew to save the .INI file.
Try to disable it and see if GSX can save now.