Whisk together Worcestershire sauce, soy sauce, lime juice, onion, red pepper flakes, dry mustard, salt, thyme, black pepper, garlic, and hot pepper sauce in a bowl; pour into a resealable plastic bag. Add venison steaks, coat with marinade, squeeze to remove excess air, and seal the bag. Marinate in the refrigerator for at least 1 hour.

Preheat an outdoor grill for medium-high heat and lightly oil the grate. Remove venison from marinade and shake off excess. Discard remaining marinade.

Cook steaks on the preheated grill until they are firm, hot in the center, and just turning from pink to grey, about 5 minutes per side. An instant-read thermometer inserted into the center should read 150 degrees F (65 degrees C).