You didn't go far enough into the article. What you've shown is max parallax error. Parallax for "eye offset" less than the max possible does depend on magnification.
From the article:
Substituting Equation 5 into above equation gives us the PE equation that is dependent on magnification and offset distance X:
Equation 6 PE @ offset X = (X) (MAG) ABS(t-p)/(p); for X < EP/2
EXAMPLE 3:
We have a 3-9X40mm scope, where objective diameter, D = 40mm, parallax range of scope (p) = 100 yards, and target range (t) is 25 yards. What is the parallax error at 3X and 9X if eyeball is 1 millimeter off optical axis at the eye relief of the scope? Again, p and t units must be the same, and X units can be anything you desire, although most people will probably use millimeters. The first thing to do is verify that the offset is less than or equal to EP/2. If it is great than EP/2, then your eyeball offset is outside the EXIT PUPIL and you can’t see any image. Using Equation 5, the EXIT PUPIL at 3X is equal to 40/3 = 13.3mm and the EXIT PUPIL at 9X is 40/9 = 4.4mm, so X is indeed less than EP/2 in both cases. Using Equation 6, we calculate the PARALLAX ERROR as:
PE @ 25 yards with a 1mm offset from optical axis @ 3X = (1.0) (3) ABS(25-100)/100 = 2.25mm
PE @ 25 yards with a 1mm offset from optical axis @ 9X = (1.0) (9) ABS(25-100)/100 = 6.75 mm
