Slaked Thirsts is different from other cards that work when stacked. It is an event, and all events have their twilight cost when you play them.
In that case, the way the card is written would never work. As a first step of playing card you have to remove it from its zone and put it into "void", then in step 2 you check for meeting the requirements, and in step 3 you pay the cost. One of the costs of the card is to discard it, but you can't discard it, as it's already in the "void". Since you can't discard it, the card has no effect.
So it's either has to be an activated ability of the card, with a cost of discarding it, or it will be played from the stacked, but then the "discard this event" part has to be removed.