Whisk 1 tablespoon olive oil, butter, onion, wine, Worcestershire sauce, lemon juice, parsley, seafood seasoning, garlic, and black pepper together in a bowl; add shrimp. Toss to coat evenly. Cover bowl with plastic wrap and refrigerate for flavors to blend, at least 15 minutes.
Preheat an outdoor grill for medium-high heat and lightly oil the grate. Coat steaks with 2 teaspoons olive oil; sprinkle with steak seasoning.
Cook steaks until they are beginning to firm and have reached your desired doneness, 5 to 7 minutes per side. An instant-read thermometer inserted into the center should read 140 degrees F (60 degrees C). Transfer steaks to a platter and loosely tent with a piece of aluminum foil.
Remove shrimp from marinade and grill until they are bright pink on the outside and the meat is no longer transparent in the center, 2 to 3 minutes per side.
