ACL comes handy here to use in this kind of situation. If your app is ACL enabled, one user can not access/use the data of other app user unless authorized. To use ACL, your app user either be authenticated using App42 User Service or through Facebook Login. If you are using App42 user service, you have to call setSessionId or if you are using facebook you have to call SetFbAccessToken as described by you.
See complete tutorial here for the same.
If you want to create a api key which can only access saveScore method or any xyz method, you can take a approach descibed by dhruvc below.