@chinn_asama,
Great question. First of all, I will remove the suspense - The sentence is correct from modifier reference standpoint. Now comes the explanation:
You are correct in saying that the modifier should be placed close to the word that it modifies. In fact this "rule" comes from the requirement that modifier reference should not be ambiguous. Here is a direct quote from official guide
Modification Problems: Modifiers should be positioned so it is clear what word or words they are meant to modify. If modifiers are not positioned clearly, they can cause illogical references or comparisons, or distort the meaning of the statement."
Now let's apply this requirement on noun modifiers - since a sentence contains several nouns, if the modifier is not placed close to the modified entity, then there will be ambiguity regarding the modifier reference.
But as you know, there are other kinds of modifiers as well. Modifiers that modify the entire clause or the idea presented in the clause and the modifiers that modify the verbs. The modifier in your sentence actually is the one that modifies the idea presented in the preceding clause and since it is placed and worded correctly, the modifier reference is absolutely clear.
Here is what the sentence means:
Since some specific time, US dollar has been used in certain specific capacity. This fact - i.e. use of dollar in this specific capacity has resulted in something - "dollar serving as the intermediary currency...". So in essence, this modifier presents the result of the preceding clause.
This is a classic use of verb-ing modifiers. When used to modify preceding clauses, they either describe the preceding clause or they present results or outcome of the action in the preceding clause.
I would suggest that in order to learn more about verb-ing modifiers, you review the concept titled "Verb-ing Modifiers". This is available in the FREE TRIAL of e-GMAT SC Course. Just register on e-GMAT and get on your way to learn about Verb-ing Modifiers. Click
https://e-gmat.com/secure/register.php to register.
Hope this helps.
Regards,
Payal
PS: One thing that surely was off in this sentence was the part "since world war II's end". Better way to write this is "Since the end of world war II".