First, note the following:
The highlighted sentence is a passive sentence. In passive sentences, the agent is often marked by に.
"なぶりもの" as a whole is a noun-equivalent, so the verb of the highlighted sentence is not 嬲る. Instead, you could say that "なぶりものにする" is like a verb on its own.
Breaking down the sentence piece-by-piece:
戦争で
the "location" of the action
敵兵に
the agent of the action in the passive sentence
なぶりものにされて 殺されたんだ
the two verbs of the sentence, combined with て to indicate that the two events happened sequentially.
The verbs are conjugated in the passive voice. The 敵兵 is the agent who is doing the action, and we understand from context that it is the speaker's 両親 who received the actions of the agent.