Discarding for cost is not the same as discarding for effect. With Dark World monsters, the card must be discarded by effect like Graceful Charity, Dark World Lightning, Card Destruction, etc...
If a card states that a card must be discarded as a cost for an effect, the effect of the Dark World monsters will not activate.
One other note to remember is that "sending" to the graveyard is also different from discarding. Prime example, The Creator's effect of sending a card to the graveyard isn't a cost, but its effect is "sending" and not "discarding", so our beloved Dark Worlders won't get their effect that way.
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