You are correct in detecting an error in this sentence. But the error does not lie in the conjunction, when rather than that, but in the tense of the verb hesitate.
This sentence is long, so let’s start by simplifying it, to make the pieces stand out:
- I reduce It argues a sad defect of information concerning the Far East to It shows ignorance.
- I reduce when so erudite a scholar as Dr. George Miller did not hesitate to affirm that, chivalry, or any other similar institution, has never existed either among the nations of antiquity or among the modern Orientals to when he said that
You believe that sentence 1, below, is ungrammatical, and should be rewritten as sentence 2:
- ? It shows ignorance when he said that.
- okIt shows ignorance that he said that.
Your rewrite, 2, is an It-cleft†: a ‘canonical’ sentence in which a subordinate clause acts as the subject is ‘transformed’ by moving the subordinate clause to the end of the sentence and replacing it as subject with the dummy pronoun it:
2a. [That he said that] shows ignorance.
2. It shows ignorance [that he said that].
Your objection to sentence 1 appears to be that a when clause is an adverbial and should not be employed as an NP argument. This objection is echoed by the old school of ‘prescriptive’ grammarians; generations of schoolteachers have tried to stamp out such uses as:
A gaffe is when a politician accidentally tells the truth.
A circle is when all the points on a curve are the same distance from a single point.
This construction is in consequence avoided in formal English. It is only formally acceptable to use a when clause as an NP in the predicate, where it is taken to be a ‘pro-form’ (like a pronoun) referring to a particular named time:
Now is when we should act.
Monday is when I expect to be finished.
And that in effect is how it is used here: it identifies the event or occasion which argues a sad ignorance of the East.
But this does not mean that when is equivalent to that as a complementizer. You cannot simply replace that with when. When clauses have two constraints which that clauses do not:
To my mind, both of these constraints are ‘surface’ adjustments made because when clauses are ordinarily temporal. That makes a difference in tenses sound odd. It also means that a when clause at the beginning of a sentence will at first be understood as an adverbial. Consequently, the it is required to clarify its role. Note that this it can also be employed with that clauses:
That he said that, it shows ignorance.
†: Some grammarians distinguish what we are talking about here from cleft sentences and treat this as a species of extraposition. On this analysis, only It constructions with be + relative clauses qualify as clefts:
It was ignorance that was shown when he said that.
I think this is a false distinction. Distinguishing clefts from extrapositions is often very difficult, so I prefer to regard the different sorts of It construction as a single species. But the analysis of clefts is very controversial.