I think you are looking for the PlayFab Master Collection. It can also be integrated into a website using the JS API.
construct.net/en/forum/construct-3/plugin-sdk-10/construct-master-collection-en-139046
It syncs your game on an allocated server for you via PlayFab service and binds/links to various ways you want. Including but not limited to Company (your company in PlayFab), Facebook, Google Plus / Play, Android, iOS, XBox, Custom ID or Cryptography, etc.
Just like that, you can also integrate it into your website, again with the JavaScript API.
I hope that helps.