For the moment, they can copy the game log and save it to a text file when the game is over and they are presented with the "The game is over" dialog. If all goes well, the next updated will make this copy look nice when made from Firefox as well as it already does for Chrome.
> I wonder what logistical/programming issue prevents this?
Always hard to tell. What may not be clear is that the game log isn't a text file that is stored somewhere on the server. Instead, it is the actions that are stored, and then the log is recreated if the game is reloaded. For exmaple, if you load the game of a game between two players who both used Chineese as their language when they played, the game will be shown in your language, including the game log.