Oh man yeah that was brilliant, I think that's to do with what Robert said earlier in the movie, I don't remember the exact quote but when arguing with his wife he says that he needs to do it and he needs to be able to look at the killer's face and stare into his eyes and know he did it.
It was something like that & I think that's why that scene with him staring at Arthur occurred, however I have no idea if he really thinks it was him, because he had a sort of look of uncertainty, however i'm pretty sure the next shot was that of his book being sold so he likely got what he wanted and believes that Arthur is the Zodiac Killer