Three degrees of rear toe-in is standard and helps keep your car going straight. Reducing it or eliminating it altogether will make your car harder to drive. I recommend you go through the rear suspension as follows;

1) Remove the rear tires and rear shocks.
2) Move the rear suspension arms up and let them drop on their own. They should drop all the way down without you touching them. If not then there is binding somewhere. Fix as necessary.
3) Ensure the rear inner hinge pins are perfectly flat and not bent. If bent, replace. You will need to disassemble to check this.
4) Ensure the outer hinge pins are also flat and not bent. Replace as necessary
5) Make sure the rear droop is the same left to right. Adjust until they are and use the setting from your manual.
6) Check the rear shocks and look for a bent shaft. If straight, ensure they compress and expand without sticking. Fix as necessary.

If all checks out, then do the same to the front suspension. Fix or adjust as necessary.

The tiny bit of slop shown in your video is normal and should not affect the way your car tracks much if at all. Shimming to the point of zero movement might make things too tight and make it worse.