In my opinion - it's valid on any route permitted for journeys from Littlehampton to any station within Zones 1-6 (unless there are any routes which leave the Zones after entering them, in which case the ticket is valid to the first station in the Zones only).
It's not quite that general. An Out-Boundary travelcard is an ordinary Travelcard with a return journey to the
boundary of the zonal area added on. So you calculate permitted routes based on the first station at which the train stops or passes within the zones, (and of course as you say must discard any such permitted routes that themselves pass through the zones as they would have a different boundary station).
AFAIK there is no official word on this
The official position comes from interpreting the TSA and the Travelcard agreement and has been quoted from ATOC on this forum in the past and is also provided to developers of routeing engines.
The reasoning goes roughly as follows. From the Travelcard agreement (1995):
Out-Boundary Ticket shall mean a ticket issued by an Operator to a passenger for a journey on Railway Services outside the Zones which includes a Travelcard to be used in conjunction with the relevant journey on Railway Services;
I.e. the travelcard covers all travel within the zones (as it must) and additionally there is a journey
outside the Zones. That journey outside the zones is from an origin to the boundary station and so for that journey outside the zones the destination "London Zones 1-6" gets interpreted as meaning the first station encountered at the boundary of the zones, and routes are therefore calculated (under the familiar rules set out in the TSA using the Routeing Guide) to that point. There is no restriction on which boundary stations to consider so the passenger can choose, but for most there will be no permitted routes satisfying the conditions. There is a small ambiguity in the application of the shortest route provision - my reading is that it only applies to the closest of the available boundary stations and for any other boundary station, you're limited to what the Routeing Guide maps give you. (In other words, there can only be one shortest route for the ticket as a whole, not one for every boundary station you might consider, but I think this remains open to alternative interpretations.)
Once you get your head around it, the documentation does all knit itself together reasonably coherently and consistently.