No, it's not a very local definition at all, it's actually a generalized definition for all forms of game and entertainment -- and art, even!

You seem to be assuming I have a reductive definition of game, when the definition given in the article is basically "anything people choose to play." See https://www.raphkoster.com/2013/04/16/playing-with-game/ which is linked in there.

I strongly disagree with lumping "intelligence" into the question though, so I am with you on that.