Due to limitations in SharePlay, it is not possible to join the game directly within the Guessing Game app. You must always use the Join SharePlay dialog to join a game.
You can invoke the Join SharePlay dialog either by going to the FaceTime app, or by tapping the green oval icon at the top of the screen when you are in a FaceTime call. If there is a game in progress, you should see the SharePlay dialog that says "Join SharePlay" with an Open button. Tapping that button will join the game. You will have to use this button to re-join anytime you leave the Guessing Game app or close the game window.
If you don't see a Join SharePlay dialog in the FaceTime app or when tapping on the green icon, then there might not be a game in progress and you will have to start a new one.