[throwaway798214]

Encode your game state to the URL itself and tell the user to bookmark that URL. User can then use browser sync, email or whatever to sync the bookmark to another computer to continue where they left off. No services, no tokens, no sharing data to some random company or person.

[Waterluvian]

A URL is about 2000 characters max, so this definitely works. It's a more portable than localstorage given they can just handle the URL themselves.

This doesn't cover collective access. Eg. high scores, though. I'm still thinking on that one. I think it's going to be impossible to find because of security implications. Services are either going to not want to make it work, or require accounts.