According to the links within this article, although the root URI of the router requires authentication, the /password.cgi URI doesn’t and the resulting returned HTML contains (but does not display) the plaintext of the password, as well as an HTML FORM to modify the password that is exploitable by CSRF.
The attack… infected more than 4.5 million DSL modems… The CSRF (cross-site request forgery) vulnerability allowed attackers to use a simple script to steal passwords required to remotely log in to and control the devices. The attackers then configured the modems to use malicious domain name system servers that caused users trying to visit popular websites to instead connect to booby-trapped imposter sites.