If the server login needs a key and password (separate from the password to encrypt your private key), yes that's two factor: the server sees something you know and something you have. I worked on a platform (Salesforce B2C Commerce Cloud) that sometimes used WebDAV with HTTP basic auth and HTTPS client certificates (combined), and that was considered two factor authentication. I don't see how that's totally different from this SSH setup.
If the server login needs a key and password (separate from the password to encrypt your private key), yes that's two factor: the server sees something you know and something you have. I worked on a platform (Salesforce B2C Commerce Cloud) that sometimes used WebDAV with HTTP basic auth and HTTPS client certificates (combined), and that was considered two factor authentication. I don't see how that's totally different from this SSH setup.