Fleeing the Navy, in Pirate's Cove
The remaining opponents get 1 Fame each.

(Quotations are from the rules (English, German))

The Scoring section is somewhat confusing in the English version:


  Pirates GAIN fame from each of the following actions
  
  
  Winning Battles (1 point per player that is defeated or flees after being hit)
  


The German version (note that the original game was German) translates to:


  
  Winning battles (one point per player whose ship has been destroyed or flees after being hit)
  


However, the emphasis seems to be on the action of a ship being disabled or a ship fleeing, not in the outcome being called "winning" a battle. The Forced retreat section follows this thinking:


  A crippled ship brings all remaining opponents on that island 1 point of fame.


And the German is even clearer:


  All opponents remaining on the contested island receive one fame point for a destroyed ship.


The fact that the word "opponents" is plural and that the German still calls it a "contested" ("umkämpften") island both refute the fact that a battle must be completely "won" by dispatching all other opponents.