Parallax is a scope issue, not a .22 issue. All scopes have a specific range where the parallax is zero.
Take a scope that has zero parallax at 100 yards. Your eye is the gun's rear sight and the crosshairs are the gun's front sight. Optically, those crosshairs are 100 yards in front of your gun. When you shoot at something 500 yards away, moving your eye does the same thing as moving the rear sight of a gun with open sights. Moving your eye left moves the point of impact left.
When your target is 50 yards away, the "front sight" is 50 yards beyond the target and moving your eye left moves the point of impact right.
When your target is 100 yards away, the cross hairs are at the same distance as the target and moving your eye has no effect on the point of impact.
Many .22 specific scopes have zero parallax at 50-60 yards, reflecting the practical hunting range of a .22.