Starting this week, a new era for prime-time cable news begins. Tucker Carlson will assume Fox News’s 8 p.m. time slot on Monday, the first time in nearly two decades that Bill O’Reilly will not be kicking off Fox News’s prime-time lineup. And Fox’s competitors are taking notice. Mr. O’Reilly’s dismissal amounts to an enormous shift in cable news, and the TV industry was ablaze with talk late last week whether the move has the potential to open up a cable news war that for more than a decade has been dominated by Fox News.