All three Dupin tales of detection feature these two guys. They're totally dependent on each other. Without G—, Dupin would have no cases; without Dupin, G— couldn't solve any cases. For that matter, Dupin probably couldn't solve many cases without G—, either, because Dupin couldn't and most likely wouldn't perform the thorough search of D—'s apartment and the surrounding area.
In spite of Dupin's condescending attitude toward G—, he knows full well that they're only complete when they're together.
The royal man and D— are in some ways foils. While D— is described as perceptive and cat-eyed, the royal man is pretty oblivious. The royal man doesn't notice that anything weird is going on with the royal lady, nor does he notice when D— steals the letter in his very presence.
And later, D— becomes the royal man's symbolic double. When Dupin steals the letter right from under D—'s nose, D— becomes just like the oblivious king. They both represent a blind lack of knowledge.