For some time now I had assumed that the "mail me all my games in pgn format" function was just broken. I had clicked it many times and never received anything, even though the page said they were being emailed to me.
The actual problem was that I had never given chess.com my email address, as it's optional for FB users. It's not that I didn't want to, I just never thought about it. It would be good for chess.com to alert the user who is trying to get downloads that they first must supply their email address.
The other small issue came up when I did go to enter my address. On that page, it asks for your password, which because I come through FB, doesn't exist here. Luckily it allowed me to enter it anyway, but it would make sense for chess.com to alter the input page to let FB users know they don't have to put in the password.