I'll try to answer your question although I'm blind to Chinese clause structure. But notice that you wrote PRO in your question. PRO is quite different from pro. Let's consider this sentence:
(1) Zhangsan bei OP tufei t dasi-le Pro baba.
The first thing to note is that this sentence is causative. You've X caused Y to kill Z, where X is Zhangsan, Y is tufei and Z is baba (may he rest in peace :) ). Y (tufei) is the killer, it should act as follows:
(2) The bandits killed my father.
(3) The bandits seemed [t to kill my father]
In (3), the subject of to kill my father is not overtly realised by the bandits, this element has raised, but still it left a trace (t) that acts as a subject of the embedded infinitival clause. What is important to us here is that subjects are subjects of clauses whether they were moved or not, subjecthood must always be guaranteed in the sentence. This is why we have empty categories in general, to guarantee predication requirements.
In (1), compare it to the tree diagram you used, you have IP1, IP2, IP3. Each IP requires a subject. We don't care whether empty/null or realised. IP1's subject is realised by Zhangsan, IP2's subject is realised by OP, and IP3's subject is realised by bandits. So far so good. Now why not using pro as subject of IP2 and why using this pro and this OP at all?
Let me start with the most embedded null element pro. Pro is an empty subject used in pro-drop languages (languages which can drop the pronoun e.g., Spanish):
(4) bebí café (I drank coffee).
In (4), there is no subject pronoun realised, its identification is recovered by agreement morphology realised on the verb. Sometimes this pro acts as an object as in your example. Pro is pronominal, it must be bound by another element to co-refer with, but this binding should be distal. I don't know the details of V+complement predication of Chinese, but I assume that something can be dropped there, mostly objects. Pro+baba forms V' which introduce the OP in Spec,V'. This is the subject that moves to Spec,IP2. It's realised in Spec,V' for predication (theta marking). Why does it move to Spec,IP2? This can be answered by assuming that OP moves to Spec,IP2 to become closer (in a local domain) to be controlled by Spec,IP1 Zhangsan. Carefully note that they share all the same index (i). Binding between pro and OP (before movement) is established at DS. Pro must not be bound in its local domain because it acts as a pronoun [+pronominal]. This is guaranteed at SS after OP moves.
After movement of OP to Spec,IP2, this binding becomes distal. Pro cannot be in Spec,IP2 because it would be locally controlled by Zhangsan. Also this position is not for objects, it's a subject position, and this pro you have at foot of the tree is an object. However, OP (null operator) is free to be bound anywhere and it also establishes the bridge between predication of the most external subject and what is embedded in a tree.