So I called RBC, and was told that it's definitely an issue on AA's end to credit the bonus.
I then called AA, and they told me that it's definitely an issue on RBC's end to credit the bonus.
(I had a hunch that would happen)
I pressed the AA agent further, and he went to talk to his supervisor, and they could find no record of this promotion. I then gave him the URL of the promotion on the AA website. He apologized, and said that they deal with a lot of promotions and it's hard to keep track of them all.
He wasn't sure why the bonus miles didn't post, other than that sometimes it does take a few weeks for the bonuses to post after the base miles. He suggested that I wait until next month, and if they don't post to call back. I made sure that he noted my account with the URL of the promo so I don't have to go through this again with the next agent.
(I should mentioned that both the agents at RBC and AA were super friendly, and were trying to be as helpful as they could.)