SNK Wikia = "The major difference from this series's continuity than others is the fact that Geese is still alive. An interview with Neo Geo Freak reveals that this is mostly due to the fact that the King of Fighters development team wasn't initially aware about Geese's fate in the Real Bout series. Once they heard about it, the developers from Real Bout team approved his appearance in the series due to their desires to create the Boss Team. Additionally, Geese's profile statistics during this series are the same ones for Fatal Fury Special (excluding his age)."
He actually died at the end of Fatal Fury Special, so 96 wasn't too unbelievable that he was there. In later versions they put him as Nightmare Geese, who was a ghost of Geese himself. Most of those games were dream matches anyways.
KOFXI was a bonus character featured as a sort of dream-match thing, like UM versions. There's no reason Tung / Big / Robert would be there. They just used characters from NGBC as a PS2 exclusive.