personally I think what's missing from your definition is that most games have an intentional lack of stakes/costs that are associated with the original process

personally I think what's missing from your definition is that most games have an intentional lack of stakes/costs that are associated with the original process they were mean to abstractly simulate. (and the focus on entertainment, at the expense of accuracy) - when a lion play with its cub the danger of heavy injury and death is minimized. - when you play chess there's no danger of you being beheaded due to a failed military strategy. - when you lose at monopoly due to failure to grasp the nature of the game or your social skills you don't end up old and destitute as a result. etc...