The problem is that "games" is one word, but we really have two core types of game. Some games focus on mechanical skills or rules akin to a sport or boardgame

The problem is that "games" is one word, but we really have two core types of game. Some games focus on mechanical skills or rules akin to a sport or boardgame, others are an interactive narrative experience. This interactive experience can further be broken down into games that tell you what is happening (cinema), and games that let you make your own story (tabletop RPG). So while there is a lot of crossover and blurred lines, of these types of game, only one type really needs a well written or scripted story to achieve its goals. We have many successful games with no story due to this, but other games wouldn't have succeeded without one.