Combine soy sauce, vinegar, sesame oil, and chili sauce in a small bowl; set aside.
In a large skillet, heat olive oil over high heat; swirl to coat pan. Season steaks with salt and pepper; cook until browned, 3 to 4 minutes per side. Transfer to a plate.
Pour off fat from pan; add green beans and 1/3 cup water. Reduce heat to medium. Cover; cook until beans are crisp-tender, 4 to 5 minutes (add more water if pan becomes dry).
Thinly slice beef. Pour soy mixture into pan; toss. Return beef and any accumulated juices to pan; cook (uncovered) until heated through. Add bean sprouts; toss to combine.