These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official and can still be correct, as long as they follow the official gameplay rules, or unless Konami has issued a ruling that says otherwise. References: 
"The Six Samurai - Zanji" does not need to remain on the field after battle for its effect to activate. Even if it is destroyed by battle, as long as you control another "Six Samurai" monster, the monster it attacked will be destroyed.
"The Six Samurai - Zanji's" effect activates at the end of the Damage Step. If there are no other "Six Samurai" monsters with a different name face-up on your side of the field when its effect resolves, the effect disappears.
These TCG rulings were issued by Upper Deck Entertainment and have since been deemed unofficial by Konami. They were previously considered official, but may or may not necessarily hold true nowadays.
↑The Ruling means that those Rulings apply to all "Six Samurai" monsters with the effect "If this card would be destroyed, you can destroy a[nother] [face-up] "Six Samurai" monster you control instead.", and "Great Shogun Shien".