Protecting sessions on possibly compromised account
There is no need to actually redirect to the login page if session management upon password change is done securely. That is, as long as all current session identifiers are invalidated and the current session is attached to a new session identifier (usually issued as a token in an authentication cookie - the cookie is only sent to the session that just changed the password) then there is no risk of an attacker who is already in the account from staying logged in.
The rationale behind the OWASP article is explained below. There is nothing wrong with the security aspect of it, however there are some usability issues.
Password reset functionality is often used when a user wishes to secure their account.
By invalidating all existing sessions upon password reset, the system is making sure that only the person with the new password can login.
Say, for example, an attacker that has gained access to the account using the old password is logged in. Resetting all sessions will log the attacker out.
Why log out the current user, I hear you ask?
Well say that the attacker is riding on the current user's session, say using a session fixation vulnerability. This means the attacker has the same session as the real user. Resetting the current session also will make sure no one is on the account who is not meant to have access.
Redirecting to the login page in your quote above is really describing the fact that you should log the user out of the current, and all sessions (but there is no risk from stopping you dropping them into a new session with a new identifier).