My best guess: Maybe signing the webhooks assumes the TLS-terminating middlewares might not be trusted? Or some other middleware between that and the final handler.
To the best of my understanding, the two options mentioned in the article require a shared secret: API keys include that secret verbatim in the request, while the signing uses the secret in an HMAC function.
If asymmetric cryptography were somehow involved, I would somewhat buy the arguments about validating the origin of the request, because only one party would be able to create a valid signature. But that's not the case here, because with HMAC both parties have access to the same secret used to create a "signature" (which is more like a salted hash, so creating and validating a signature are the same process).
So, if both parties can produce the hash for a valid signature, and the secret is known to both ends, and there's no advantage over API keys when using TLS (assuming TLS is not broken), then I can only think that the problem is what happens outside TLS.
That's why I think the threat model would be a compromised TLS-terminating proxy, or some compromised component in between TLS-terminating proxy and the final application handling the request.
Sounds like zero-trust shenanigans.
If I'm misunderstanding anything, I'm more than happy to be corrected.