By RAW, the Druid does not die
In my opinion, Rules as Written, the Druid would not die. This is supported by the actual text. Unlike the current top answer for this question, there is nothing in the text to support the idea that Power Word: Kill "bypasses" Wild Shape. There is no separation or distinction between the Druid and Wild Shape. You can't target one without affecting the other.
The Druid under Wild Shape gains the effects of what's written in the text of the ability (same with Polymorph spell). This includes the effect that the Druid (or person under the effects of the polymorph spell) would revert back to their natural form with the same number of hit points they had BEFORE they were under the effects of Wild Shape or Polymorph. The trigger for this effect is if they would be reduced to 0hp or die.
Since Power Word Kill specifies that they would cause someone to die, it would trigger the effect of Wild Shape or Polymorph and revert the druid (or person affected by Polymorph) to return to their original form with a number of hp they had before they were Wild Shaped or Polymorphed.
I understand that Jeremy Crawford Tweeted about this, however the actual text of the book does not support this statement. Perhaps that was the rules as intended, but it is not the rules as written.
In order to conform to what Jeremy wrote, the clause in Wild Shape and Polymorph that includes death as a trigger should be removed. That is the only way I can see that would support this interpretation.
Just going to re-post Jeremy Crawford's response on Twitter below:
*Bobby the Barbarian: If a druid wildshapes into a wolf and is then targeted with power word kill does the druid revert dead or alive?
Jeremy Crawford: If you have 100 hp or fewer, power word kill causes you to die. Notice that it doesn't say you drop to 0 hp.
Airatome118: So what is PHB pg. 66 "You automatically revert if.....drop to 0hp, or Die ." telling us? Form dies, Druid reverts, yes?
Jeremy Crawford: Beast form ends if the druid dies; things like power word kill can end you without reducing hit points."*
The problem with this exchange is that Jeremy seemingly makes no indication he remembered/realized that Wild Shape and Polymorph triggers on when the Druid dies as well as if they would reach 0hp. He only mentions the 0hp trigger.
Though I appreciate Jeremy's answer, I would have to very much disagree that this is a correct ruling as the text within the book does not support this statement and I have reason to think he simply forgot or wasn't paying attention to the fact that Wild Shape and Polymorph have a second trigger, not just from reaching 0hp.
So, again, the only way to support the idea that the Druid would die as a result of Power Word Death or would be if the clause where you automatically revert if you die is removed. Because that is literally the only kind of stuff that the clause of the power CAN affect. Not a whole lot of things out there just outright kill you. Wild Shape and Polymorph specifically address this.