World legacy Key Ruling

The correct answer is that because "Fiendish Chain" is a continuous card, it will continuously attempt to apply its effect. Furthermore, "World Legacy Key" can only negate activated effects. An activated effect is an effect which has been activated(in other words, the effect resolves, i.e. it reserves a chain link). In this case, you only negate the instance of that activated effect. In other words, the effect which was activated, right before it resolves it will be negated by the negating effect. So model wise it looks like this:

Building Chain

Chain Link 1: "Fiendish Chain"

Resolving Chain

---> Begin resolving chain ---> Begin resolving "Fiendish Chain" (intercepted by "World Legacy Key" ), which negates the activated effect of "Fiendish Chain". The activated effect of "Fiendish Chain" is to negate the effects of 'that' face-up monster while it is on the field.

-->[ empty resolution, resolve without effect ]

--> End resolution of "Fiendish Chain"

--> End resolving the chain / "Fiendish Chain" reapplies and continues to negate the effects of the targeted monster. (Continuous cards will always try to apply their effects, even if negated). A negated effect doesn't mean the effect is non-existent. It is there and will apply their effects once the restrictions have been lifted.

Your question seems as though "World Legacy Key" was face-up for the entire time that "Fiendish Chain" was, and even in that case it doesn't matter. The activated effect should be thought of as an instance of activating, so you are only negating the effect when it resolves. With something like "Altergeist Kunquery", if you negate its activated effect, it will not continue to negate the effects of the monster. You can say it continuously targets the monster, but that doesn't mean it will continuously try to apply its effects, that is because it doesn't have a continuous effect', so the negation depends on whether the trigger effect resolved 100% proper.

Let's start from the beginning, "World Legacy Key"'s effect stated:

Negate any opponent's Trap effect that activates in the same column as a "Mekk-Knight" monster you control.

Assuming this Continuous effect already took place, your opponent activates "Fiendish Chain" with this activation condition:

Activate this card by targeting 1 Effect Monster on the field; ...

Which will now be explained by this article: Activate

1. A card or effect can only be activated if that card or effect meets its activation conditions.
2. The activation cost for a card or effect must be paid in order to activate a card or effect.
3. It is not possible to activate a card or effect if the effect would fail to do anything when it resolved.
4. It is not possible to activate a card or effect if it has no valid target.

Number 3 does NOT actually stop "Fiendish Chain". It means fail to do anything by the game mechanic or does not change any game state if it resolved, not negated by card effects (for example, activating "Raigeki" or "Dark Hole" when there are no monsters in the field). It is perfectly fine to activate cards as long as the activation condition is met, regardless if it would be negated by even Continuous effects.

Additionally, "Fiendish Chain" continuously targets the targeted monster, therefore as soon as "World Legacy Key" is no longer active, "Fiendish Chain" will automatically negate the targeted monster at the time of activation.

Therefore, "Fiendish Chain" can be activated, but its effects are negated as long as "World Legacy Key" is active. "Fiendish Chain" will remain on the field.

According to Shinji's explanation below, "Fiendish Chain"'s Continuous Effect still negates according to this ruling about "Skill Drain", so yeah, my bad. Kudos to him for finding the ruling in Japanese. Sometimes Konami make everything more convoluted than it should be.