In a 9-by-13-inch baking dish, whisk together soy sauce, sugar, vinegar, Worcestershire, mustard, red-pepper flakes, and pepper. Place steak in dish and cover dish tightly with plastic wrap. Swirl dish so that marinade coats the top of steak. Refrigerate 1 to 2 hours, turning steak occasionally.
Heat grill to high. Remove steak from marinade, letting excess drip off. Pour marinade into a saucepan and simmer over medium-high heat until reduced by half, about 10 minutes.
Clean and lightly oil hot grates. Grill steak, covered, 6 minutes; turn, brush with glaze, and grill until medium-rare, 6 minutes more. Let rest 8 to 10 minutes before slicing.