Parallax could be defined that way, but the effect in shooting context is as if you viewed your automotive fuel or temperature gauge from straight on, vs the passenger seat - the reading will not appear to be the same from both viewpoints.
In a rifle scope, parallax occurs when your reticle is not on the same focal plane as the target. Eye movement behind the scope equates to the target moving out from under the reticle. When this occurs, and the reticle is then realigned from the new eye position, your zero is affected and the group center moves. When both reticle and target are on the same focal plane, the image is said to be "parallax free" and eye movement is not critical to point of impact.
You actually refer to scope/sight "offset", in which the axis of the scope (parallax free or not) or sight plane is offset from the axis of the bore. This is more troublesome at very close ranges.
An AR-15 for example, has high-mounted sights with a rather large sight offset of 2.5", many scoped rifles will have 1-1/2" to 1-3/4", and a shotgun with a plain barrel & bead will have less than 1/2" offset.
The effect is that, when we have a large offset, the barrel must be pointed up more steeply of coincide with the line of sight.
An AR-15 with a 55 grain .223 can be zeroed at 25 yards, and will be so steeply inclined that it will cross the line of sight again (be zeroed) out around 250 yards, with a midrange trajectory of around 2".
By comparison, a low-sighted bolt gun shooting the same ammo, with a small offset of only 1", can be zeroed at 25 yards and it will again be zero at 105 yards, and midrange trajectory is close to 1/4".
