In a 2- to 3-quart pan, combine vinegar, sugar, wine, catsup, Worcestershire, onion, cornstarch, rosemary, hot sauce, 1/2 teaspoon salt, and pepper. Stir over high heat until boiling, about 2 minutes. Let marinade cool, or to chill quickly, nest pan in a bowl of ice water and stir until cold, about 5 minutes.
Rinse steaks, pat dry, and put in a 1-gallon heavy plastic food bag. Pour marinade into bag, seal, and rotate to mix well. Chill at least 1 hour or up to 1 day.
Lightly oil a barbecue grill over a solid bed of hot coals or gas grill on high heat (you can hold your hand at grill level only 2 to 3 seconds). Lift steaks from marinade and lay on grill. Close lid on gas grill. Pour marinade into a 1- to 1 1/2-quart pan.
Turn steaks every 2 to 3 minutes to brown evenly, basting with marinade up until 2 minutes before meat is cooked to desired doneness, 10 to 12 minutes for rare (cut to test). Stir marinade in pan (on grill or over high heat) until boiling. Spoon sauce onto steaks; season to taste with salt.