It must have been incompleted. (￣ ￣|||)

No, you can't replay it once you complete. But if you don't complete it, when you win the fight, quickly close your app, and when login back, retreat from the fight.

The youtubers in question have alt accounts where they leave certain fights like this one and Goetia for example, incomplete. They finish the battle and close the game before they claim battle drops. That way, they can borrow the servant from their main accounts, and do the solo runs whenever a new servant gets released.