From watching the linked video, and going by the given informal definition for NP-Problems "hard to compute, easy to verify" I think of it this way:
You can not compute the secret number efficiently, only the keeper of the secret knows it. So the number is indeed hard to compute. But can you easily verify a solution? Sure you can ask the keeper and he can tell you the answer, but then you didn't verify it yourself. If you count on the secret keepers cooperation he could also just tell you the number, making it easy to compute.