The same profiles you use to watch Netflix are also used for Netflix Games.
When you launch a game, choose your profile. Game progress will be saved under the chosen profile.
Some games use cloud saves and you can continue from where you left off on any device with the same account and profile. For more, see How do game saves work on Netflix?
If you delete a profile, you’ll lose both your game saves and the info about what you have watched or saved to My List for that profile.