Just launch version 7.x-1.7 of the League Module.
After a lot of reading, writing and testing, finally integrated with OG, Context and PURL.
Have to program a small "spaces" module.
Activate OG, Context and PURL
Define a Tournament Content Type (Node) and set as OG Group.
Goto Configuration -> Organic Groups -> OG Context /admin/config/group/context and check OG PURL.
Define Game Type, Person Type and Team Content as OG Content. League entities already integrate OG on its Type Form.
Create each tournament and define its URL preffix.
So if you define a tournament named Champions League and set its URL Preffix to champios, each Game, Person and Team you create under OG Champions League will be preffixed with champions, resulting as champions/game1, champions/player1 or champions/team1.
Using OG Permissions CRUD operations could be controlled by Tournament also.