That's the exact argument...
If you buy a book from GoT, you own the physical pieces of paper the book is printed on, not the words. The reason it costs more than blank pages, is the words printed on there. But you don't "own" the words. Just the pages that have the word printed on.
If you buy an electronic copy, you don't "own" anything except the rights to have a copy of that.
Same for games.
You don't "own" the game, you own the physical media the game is on. If there's no physical media, then there's nothing you own.
The reason it's the same for games and books, is why it's the same for TV, music, and every other form of media.