My take on it as a judge would be that it would depend on the blocks used to build the tower. If they are simply cubes for example, then I would says its building + artillery. If they aren't plain cubes (or there is a handicap when building - simluated shakey hand for example) then I would say its puzzle + artillery. The fact that there is a time limit, doesn't, in my opinion make it one or the other

Either way, you have at least two colours from the genre list. But I guess it would be nice if WILL or Savage could confirm how they see it as they are ultimately in charge.