This depends on an interpretation of the routeing guide.
Trains which run directly, ie. without change of train, between the origin and the destination are always valid. So London Bridge - Victoria via Denmark Hill, or via Crystal Palace, are valid routes on through trains. The permitted route via Crystal Palace provides interesting reduced price season ticket opportunities, if passengers are willing to be restricted to using through London Bridge - Victoria trains only.
As the OP implies, the shortest route by rail is always valid. For this journey, the shortest route depends on the definition of a station at Waterloo. If Waterloo and Waterloo East are regarded as one station (they are within the same station complex) then shortest route by rail at 7.75 miles is London Bridge - Waterloo East - Waterloo (within same station complex) - Queenstown Road Battersea - Clapham Junction - Battersea Park - Victoria. If Waterloo and Waterloo East are not regarded as one station (they have separate station codes) then shortest route by rail at 8.75 miles is London Bridge - Denmark Hill - Victoria.
The routeing guide also states
Therefore London Bridge - Victoria via Denmark Hill is always a permitted route, even on trains which are not direct.
It is likely that a London Bridge - Victoria ticket is valid to Waterloo East using the shortest route rule. Whether the ticket continues to be valid from Waterloo East to Charing Cross depends on interpretation of the second sentence of the routeing guide rule above. There is a need for interpretation because the rule does not specifically deal with the position where both origin and destination stations are themselves members of the routeing point group. There are 19 members of London Group for routeing purposes. The question is whether, when travelling between two members of the group, one can choose a third member to be the routeing point for the purposes of the second sentence above? My inclination is that the answer is no, because if one can choose a logical station such as Charing Cross, there would be nothing to prevent the choice of an illogical member of the group such as Bethnal Green, where the journey by rail only would be tortuous. But who said the routeing guide was logical? I would be happy to be shown to be wrong.
John