The ZK property absolutely doesn't matter. Imagine that instead of passwords the client stored a private key, and transmitted the associated public key to the server. Then when logging in the server sent a challenge and the client signed the challenge with their private key. The server then validated the signature against the public key for the user. This is absolutely not a zero-knowledge proof, but is a definite proof-of-knowledge since you've proved you know the private key.

Zero-knowledge proof (soundness, completeness, zero-knowledge) is a subset of proof-of-knowledge (soundness, completeness), so your last statement is true by definition.