TOKYO—She launched herself off the vault, stuck the landing and saluted, then MyKayla Skinner heard the roar from her teammates watching in the stands. One voice seemed louder than the rest—Simone Biles, rooting for Skinner in what would become a silver-medal winning performance. “I knew she was going to be the loudest one in there tonight,” Skinner said. Skinner had always dreamed of competing at the Olympics, and described the unexpected, 11th-hour opportunity as a “one in a million” chance that she was not going to waste. She was not supposed to be there, competing on vault in the women’s event finals Sunday. She had the fourth-highest score during qualifications. But the rules allow each country a maximum of two athletes in the finals. Biles and Jade Carey finished first and second, pushing Skinner from the competition. She was devastated that her Olympics—and her gymnastics career—appeared to have ended at …