"Playing by Appointment" means that instead of you deciding when to play, the game decides for you. If you don't play according to the game's schedule you are penalized. This dark pattern can be implemented in different ways.
1) Some games have a competitive leaderboard where you can climb the ranks by beating a player above you and taking their spot. At a certain time during the day, awards are given out based on your rank. Because of this, playing in the minutes leading right up to the "payout time" is necessary to ensure you get a good rank and aren't bumped down at the last minute. Often, the requirement to play at this specific time is not convenient and it can be stressful to a player to be unable to play during this time window.
2) Some games have special events that occur during specific times. If you want to participate in the special event, you must play during this time window. Players who work or travel may be unable to play during these time windows and will miss out and feel stress.
3) Some games use the time of day to change aspects of the game. Maybe certain items can only be collected at night. This forces people to play the game during times when they might not otherwise play.
4) Some games use a mechanic called "Harvesting" which can be implemented in many ways, but in general the player starts an action that will take some long time to complete. The player must return to the game at some specific time in the future to collect the reward. Sometimes, the reward is lost if not collected in time. In a worst case scenario, a player may set an alarm to wake up in the middle of the night just to collect the reward and then go back to sleep. This is related to the Wait To Play
These are the main ways that games use this dark pattern, but there are certainly other ways that games can use appointment times to force people to play the game at times when they may not want to play the game, but do so because otherwise they will miss out or be penalized.