당하다 puts you on the receiving end of something unwelcome — being overpowered, tagged, tricked, or floored by something. -게 says how it went: 억울하게 당했네 (you got done over unfairly), 호되게 당한 민식이 형 (took a real beating, here from the spice), 제압을 쉽게 당하냐 (how do you get taken down that easily?). One line stretches it as a joke to something neutral — 캐스팅은 어떻게 당하는 거예요? treats getting cast as something done to you.