Cave Door

In https://youtu.be/n7v0uEupkiE?t=328, he's saying simply knowing the passcode to the gate (and using it) without revealing the passcode, counts as a zero-knowledge proof.

Ali Baba Cave

Wikipedia's The Ali Baba Cave seems significantly more complex. The verifier has no knowledge of even if the verifier has gone through the gate. It is only through multiple attempts at this that the Peggy knows the word.

If they were to repeat this trick many times, say 20 times in a row, her chance of successfully anticipating all of Victor's requests would become very small (1 in 220, or very roughly 1 in a million).

Why the difference?

Is the video's example of a zero-knowledge proof still valid? If so, why does Ali Baba cave have so many more requirements?

My best guess currently is that Ali Baba Cave tries to hide two things:

Peggy does not want to:

1. reveal her knowledge (the secret word) to Victor
2. reveal the fact of her knowledge to the world in general

Whereas the basic "Cave Door" just tries to do (1)?