Place tofu slices on several layers of paper towels; cover with additional paper towels. Let stand 20 minutes, pressing down occasionally. Combine Ginger-Sesame Vinaigrette, cilantro, and soy sauce in a 13 x 9-inch baking dish. Remove 1/4 cup cilantro mixture; set aside. Add tofu to dish in a single layer, turning to coat. Cover and marinate in refrigerator 30 minutes, turning occasionally.
Prepare grill to medium-high heat.
Add lime slices to marinade, turning to coat. Remove tofu and lime slices from marinade, reserving marinade. Place tofu and lime slices on grill rack coated with cooking spray; grill 2 minutes on each side or until browned and thoroughly heated, basting occasionally with reserved marinade. Spoon 1/2 cup rice onto each of 4 plates. Top each serving with 2 tofu slices and 2 lime slices; drizzle each serving with 1 tablespoon reserved cilantro mixture.