Short version: hidden on children's accounts by YouTube's design — here is the full picture for parents.
How it actually behaves
- YouTube Kids app: no Playables at all — the section doesn't exist there.
- Supervised accounts (Family Link): the Playables shelf is hidden; direct game links
don't work either. This is by design — YouTube treats Playables as 13+ content.
- Regular accounts: full access, and game progress saves to that account.
So the «parental control» for Playables is the account type itself. If you're
deciding whether to let your kid play on a regular account — the honest parent's guide is at
Playables for kids, including hand-picked calm games.