Notably, the “legend rule” does not cause any permanents to be sacrificed. They are simply put into their owners' graveyards.

Ruthless Deathfang's triggered ability will trigger whenever you sacrifice any creature, including Ruthless Deathfang itself. It will trigger whenever you sacrifice a creature for any reason, including to pay a cost or as the result of a spell or ability (such as an opposing Ruthless Deathfang's ability).