Theoretically any game is endless and therefore just a digital playground.
Video Games aren't the only types of games; they're just an application of technology.
Chess (take the other player's King piece), Football (finish the game with the most points), Texas Hold 'Em (be the last standing player) and so on all have very definite ends goals. The same goes for games like Super Mario Bros. (finish all the levels), DOOM (in multiplayer, the game ends when somebody makes enough kills or the timer expires), Need for Speed: Most Wanted (finish all the races in first) and so on.
Yes, you can restart a game, or play from a point of the game where you left off, but that doesn't mean that the game itself doesn't have a definite end.
Being able to play curling with the Gravity Gun in Half-Life 2 isn't a selling point or something you're intended to do, but whether intent of the creator matters depends on the person playing the game.
You said it yourself; it's not a part of the intended game experience and so therefore it doesn't actually change the "game" at all; it just gives the player something else to do in the space of a game. In Soccer, players often do dances when they successfully score, and some players might play really slowly if they're winning and want to prevent the other team from scoring if they are close to the end buzzer. Those aren't intended parts of the game, but they don't prevent the game from continuing on once the players are ready either.
A player may choose to bend and modify the rules to their heart's content, but that isn't part of the main game experience that has been selected by the designer for the player to play and it's something you must actively make a choice to do. When you're finished doing that activity, the actual game experience will still be there waiting for you.
fundamentally the creator does not imo have the right to say that the feelings you got from your experience or the experience itself when talking about video games were wrong.
The Game Designer has a responsibility to build an experience that teaches you
something (a skill, some theory or whatever), and to accomplish that, we make a goal and introduce challenges that prevent a player from achieving that goal until they can successfully learn and demonstrate whatever the game designer wanted to teach.
The Game Designer doesn't have any right to comment on if the player is "playing their game wrong", since there's no such thing. In that case, it means that the designer failed to make the rules clear enough.
If you enjoy a part of the game that's not intended (as I have done a lot in the past), that's fine. That doesn't change the fact that games, as there core, about about progressing against the odds towards something specific, because that's at the very core of how we as humans operate. We are always giving ourselves goals/things to do because we don't like wasting energy, even if "something to do" means sitting on a couch napping or watching TV.
