@RoiEX Personally I find both IDs (thread-ID and game-ID) extremely useful. While I understand the desire to keep things as easy as possible for every user, those IDs are handy for searching and sorting topics/mails (as @redrum said, too).
Just one of my use-cases of thread-IDs: When testing pre-releases or creating/testing scenarios I always post fragments of games into one of my "test-threads". So whenever there is any fragment I want to post to the forum, I use one and the same thread-ID. I would not want a new topic for every case, then.
So when thinking about hiding the topic-ID from the user I would welcome very much an option to enter a given ID into the UI in order to continue posting there whatever I want. Other players would maybe welcome the opportunity to post multiple games into one and the same thread.
Thinking a step ahead we could potentially also have the engine close a topic once somebody wins the game, to be cleaned up by admins. (Can potentially be automated, or half-automated (requires button click) via a custom plugin too).
In that case we should also consider how to keep/archive the very last savegame of every game.