The language on the card is strange to me. It reads as an action that can be used at any time but the text makes reference to a 'participating character' as if it was a challenge action. I couldn't find a thread about this and wanted to know whether it is actually supposed to be a challenge action. Card text below.

Action: Kneel a Dragon character or Daenerys Targaryen to choose a participating character. Until the end of the phase, that character gets -4 STR and is killed if its STR is 0.

The card is an Action, so can be played during any Action window.

Of course, since it chooses a "participating character" as a target, there must be challenge currently in progress in order for the target requirement to be met, but that really doesn't change the "Action" designation one way or the other. The "Action" itself doesn't need to be limited to a "Challenge Action" in order to "match" the target requirement. The event would play the same, either way.

That said, the fact that Dracarys! is an "Action" instead of a "Challenge Action" creates one interesting possibility -- that is meaningless in the current card pool. If an ability or mechanic is ever created that allows a player to initiate a challenge outside of the challenge phase, Dracarys! could still be used (since it isn't limited to the challenge phase). While no such effect exists in Second Edition right now, they did exist in First Edition, so you never know.