There are more than one ways to know the game's running state.
1. If game is already started and you call the startGame then it will return BAD_REQUEST.
2. A user who is starting the game can add the room property "HasGameStarted"="true".Next user can join the room
using matchmaking api JoinRoomWithProperties() or after joining the room can check the room properties.
3. If game is already started and any user joins the room,he will get onMoveCompleted event within the TurnTime.