The "Refugee" scenario.

When the yellow player was defeated, there was no cutscene, just a message saying that the yellow player left the game, and you captured a lot of artifacts.
Do I have to replay?

You don't have to replay!
First, make sure that the necklace is among the many artifacts (it will most likely be there), then go to the prophet who asked for money at the beginning of the mission; he will give you a new quest (about the crystals), and the quest will automatically be marked as completed.