I used to be the buyer for a video and game rental store. Before people corrupted the meaning of the phrase, it had to do with investment potential. Yes, exactly like how "AAA" is used in financial matters.
I used to get catalogs from major wholesale video and game distributors (oddly, there is a porn distributor that still sends me catalogs). Many of the games were rated with AAA, AA, etc. It was a way for retailers who didn't know much about gaming to select key releases with a high ROI.
It had absolutely nothing to do with how much a game cost to make but instead with how much a game was projected to earn.
It's kind of funny now to see people calling big budget flops AAA. I remember specifically some 3DS titles being rated AAA. I remember Pokemon being AAA and, I'm pretty sure, Kirby. It wasn't rare to see games like Cooking Mama rate an AAA, as well.
So, yeah, this is really a case where people who didn't know what a term really meant creating their own definition and then everyone else repeating it as gospel until it effectively replaced the original definition.