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My question is with reference to the GNSS based separation specified in ICAO Doc 4444. Could someone explain the significance/meaning of the condition "zero offset between two waypoints" criteria?

if an aircraft had deviated, say due to weather, but is able to proceed direct to a particular waypoint, can the GNSS based separation still be applied with respect to another aircraft if we are able to establish that the two GNSS tracks are 15-135 degrees apart (but not on route)? It is this context, that I wanted to know the significance of "zero offset" clause.

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    $\begingroup$ Provide a link to where this is stated to give us all context. $\endgroup$ – Ryan Mortensen yesterday
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GNSS units have the ability to fly an offset, meaning a track parallel to the one drawn between 2 waypoints. For example a left offset of 5 NM means the track is now 5 NM to the left of the original track and running parallel to it.

The lateral separation minima specified in 5.4.1.2.1.2 for two aircraft (both GNSS) on intersecting tracks require that neither be flying such an offset – since the tracks intersect at a common waypoint that is used for separation, an offset would change this common waypoint. Here's a crude representation (blue track is an offset):

enter image description here

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