Larry L. King, a journalist, essayist and playwright with a swaggering prose style and a rollicking personal one, who left Texas as a young man but never abandoned it in his work — turning out profiles of politicians, articles on the flaws and foibles of American culture, searching autobiographical essays and, most famously, the book for the Broadway musical “The Best Little Whorehouse in Texas” — died on Thursday in Washington. He was 83.