I would like the my games screen to not just show when it is your turn but to also include icons for if you have unread private messages in a game and if you are the only player who hasn't gone (instead of just being your turn).

It should be a priority to move in a game where everybody is waiting for you over a game where you are one of 8 players who haven't gone yet.   But the My Games screen doesn't communicate that and just goes by turn time.  Maybe make the Play Game button red or flashing.