MANCHESTER, N.H. — Donald Trump was projected as the winner of the New Hampshire Republican presidential primary Tuesday, easily outdistancing his rivals, claiming his first victory and firmly establishing himself as the candidate to beat. The billionaire businessman ran away with the contest, winning across all demographics, including committed Republicans and independents, conservatives and moderates, and regular voters as well as first-timers. He doubled the tally of the second-place finisher, Ohio Gov. John Kasich. Behind Mr. Kasich were Sen. Ted Cruz of Texas, former Florida Gov. Jeb Bush and Sen. Marco Rubio of Florida. Mr. Trump, meanwhile, showed he could...