You did, and that licence comes with plenty of terms that can restrict or revoke your access to that game.
Which shouldn't be allowed, but it is.
In an ideal world, you wouldn't have to purchase a license to the game at all. You could purchase the game itself by receiving a packaged copy of it along with a copy of the source code.
That was my point -- I was building off of what you said...
I paid for a license for a game. Thus I paid for a game.
This is exactly the problem. This should be true, but it isn't in most cases.
Store's like GOG get much closer by giving you a DRM free copy. But some would say that even then, if you aren't allowed to modify and distribute that, you don't really own the game either.
A Lightyear?