No, the games stack up. Every Monday we get 2 new games, and all the prior games stay on the device. A Playdate has 4GB, and games are pretty small, so there’s lots of room. Panic has this documented — https://sdk.play.date/1.11.1/Inside%20Playdate.html#_game_si...

You can delete games and then download them again. Panic fully supports sideloading games, too.

From their FAQ:

Q: Do games get deleted when the week is over? A: Absolutely not. You keep the games forever.

https://help.play.date/games/season/