In checking the tournament standings for the 2nd chess.com 2001-2200 class I noticed that group #5 had a player that apparently resigned before making a move.  Should this entitle the four other players in the group to 2 victories apiece?

Nobody I know likes to claim a win like that.  And, if asked, the players in question would probably agree.  I am aware that we live in a world with too many rules already, but as online tournaments evolve maybe we should adopt a rule for this oversight.

The player who resigned may have been faced with any number of personal issues that prohibited play -- things happen unexpectedly.  But for those that would like to emerge from a tournament as a victor in a long fought battle should a "no move, no game" rule be placed on the books?

If every game was resigned before moving then it doesn't advantage any player over the other and counting or not counting the games has no affect on the outcome of the tournament.

What would be worse is if one player resigned all games except against one opponent. 

No way, resigning is part of the game no matter when it's done or under what circumstances.  

Understood on my original question.  The the wins are cancelled out by the fact of equality.  You raised a good point concerning selective resignation  although it seems that a player would have to be a little sick minded to do such a thing.  There's no rhymne, reason, or reward for it.  Still, stranger things have happened