If you are looking for the official story of that era, you might want to look into , which was the actual 10th-anniversary game released by SNK and kicked off the "Ash Saga" storyline.
While the phrase " The King of Fighters 10th Anniversary " is often found on sites offering "free downloads" of the game for PC, it is not an official, standalone game release by SNK. Instead, it is a . If you are looking for the official story
: Some versions allow you to play as boss characters like Goenitz or Orochi Iori immediately. : Some versions allow you to play as
: Characters from various sagas—some of whom were supposed to be dead or missing in the official timeline—are brought together for one massive tournament. It follows the "Dream Match" premise of the
Because it is a modified version (hack) of an existing game, it does not have a unique, official story of its own. It follows the "Dream Match" premise of the original KOF 2002 : The Plot: A "Dream Match"
Since this is a fan-made hack often played on emulators, the "story" experience changes through gameplay tweaks rather than new dialogue: