A more apt analogy would be efforts to restrict cigarette advertising. Book burning was about eradicating a cultural heritage, and was accompanied by a literal genocide in the case of Nazi Germany.

Although in this case, the action to remove the proverbial cigarette ads was taken voluntarily by the private media (magazine/etc., in the case of the analogy), and not done as a result of government coersion.

The analogy is really disingenuous at best, and pretty stupid at worst.