Yes that is how ownership works. Buying a game on playstation does not mean you own it on Xbox.
I think they are asking if the full version will be released on here for those who already bought it. Or do we need to buy it on steam to get be able to play the full game?
That should go without saying. Buying here gets you every update and patch as you own the game. You won't however get keys to other stores as well.
