Well, that didn’t help much. Definition 1 is pretty vague, definition 2 refers uses “game” to define “game”, and definition 3 still seems too abstract. There’s two words that stand out to me in definition 3 that get the wheels in my mind turning: “competitive” and “rules”. “Competition” can mean players playing against each other or against the game itself – either way works. It’s not quite that simple. This is a complex philosophical question, as well as an incredibly semantic one. In fact, spending a lot of time defining “game” doesn’t mean all that much if your first language is German, French, or Swahili. The dictionary definition assigned to your version of the word “game” would be different, as would the social complexities associated with the word.