Missile is a dog that understands the concept of this game and the choices he is making at night. I find it difficult to believe that an announcement that caused everyone to literally cry out in astonishment would be something he would choose to simply ignore.

Even if he did, you're saying Missile isn't intelligent enough to understand Levi... but he was intelligent enough to leave Aya and K those clues on his own without prompting? I would say the latter requires critical thinking and problem solving abilities, which are higher levels of cognition.