<aside>It looks right to me. The adjectival clause describing the OS says "the Chinese government wants the OS to replace Windows". There's an implied "that" between "the OS" and "the Chinese government".</aside>
The subject of the second clause is 'the Chinese government', the verb 'to want to', the object 'replace Windows'.
This whole thing qualifies the first clause, 'the OS'.
But the semantic relation between these two clauses ("with") is not established.
It's like saying "A detailed look at the mountain John wants to dance with an elephant".
Doesn't make sense without the "on" which links the two bits. </aside>
PS: Excuse my pedantry; this stuff really interests me.
You are right that the sentence is ungrammatical if you take the object of "want" to be "replace Windows" and the subject of "replace" to be "the Chinese government". But it is grammatical if you analyze it as an instance of the construction "X wants Y to Z", where Y is (semantically) the subject of the infinitive Z.
To a first approximation, relative clauses in English are formed by taking a sentence and moving some noun phrase to the front, while optionally adding "that" after the moved noun phrase.
E.g., "I saw the man" -> "the man that I saw _" (where _ marks the place where "the man" would have been if it was a regular sentence; called the gap or trace in linguistics.)
In this case the transformation is "the Chinese government wants the OS to replace Windows" -> "the OS that the Chinese government wants _ to replace Windows."
I agree it sounds somewhat awkward.
Excellent explanation, thank you canjobear! (And jameshart).
"Look at the car I want to buy." "Look at the horse I want to win the race." "Look at the OS I want to replace Windows."