This can happen if you tap the widget more than once too quickly. I hope that Apple changes this behavior in the future, but for now it is best to try to make sure not to double tap or tap the widget quickly in succession.

Apple doesn't allow widgets to update without user interaction very often to conserve battery life. When your opponent makes a move, we attempt to update the widget to reflect this, but often the system will not update due to these restrictions. The widget will update by itself eventually, usually within 10-15 minutes.

You can manually update the widget by tapping it to force it to update; even just tapping on the player names should do it. Just be sure not to accidently make the next move when you do that. You can also try the Refresh button in the Action menu to force the widget to get the latest game from the server.

The widgets are intended for casual play. If you would like to play an opponent in real-time it is better to play the game in the app where it should update immediately.