I think the point is about parallel vs serial layers of security. In a typical website account that is protected by password and SMS OTP, both of them need to be compromised for a bad actor to gain access. If they have just the password, they'll get stuck at the SMS token, and if they intercept an SMS OTP, they won't be able to get to the form where they can enter it. In contrast, a password-protected SSH key isn't pure MFA. If they have the password, they still need to get the private key file before they can use it to get the private key. However, if they have the private key, then they don't need the password at all. The password only protects you from people stealing the file, not from the stealing the key itself.

Compromised, meaning someone has the key in an unprotected format, or they somehow got your password. Say someone manages to MITM you somehow and get your password to the file, or they manage to crack it, or phish it out of you. Then they can just take the key and use it freely to log into your things. With MFA, there's no way that any key can be used to log in as long as the other factor exists. If you have to push OK on your cell phone to log in for example, the key is useless without physical access to your phone.

I'm not saying the password protection does nothing, it makes the key harder to crack but it's not another factor. It's simply an extension of the existing key. In other words, it's just a longer password.

It's an extra layer, but is that really another 'factor'? MFA would prevent someone with a compromised key from logging in. Password protected keys do not.