Gaioz Nigalidze’s rise through the ranks of professional chess began in 2007, the year the first iPhone was released. In hindsight, the timing might not be coincidental. On Saturday, Nigalidze, the 25-year-old reigning Georgian champion, was competing in the 17th annual Dubai Open Chess Tournament when his opponent spotted something strange. “Nigalidze would promptly reply to my moves and then literally run to the toilet,” Armenian grandmaster Tigran Petrosian said. “I noticed that he would always visit the same toilet partition, which was strange, since two other partitions weren’t occupied.” Petrosian complained to the officials. After Nigalidze left the bathroom...