It depends. There are types of games where the story is very important and others where it isn't.
For example, a visual novel or interactive fiction will be good or bad depending on the quality of its story.
In games like RPGs, the story can make the difference between an average game and a memorable one.
In arcade-style games, the story is merely decorative.
It's impossible to give a single, simple answer because the importance of a story within a game depends heavily on the gameplay style, as player expectations change depending on the type of game they're looking for.
A general piece of advice: never try to force a player to read or follow the story. Try to be friendly and give each player the option of whether or not they want to read the story of your game.
For example, never force your players to read or watch an introduction that explains the story; always try to make it optional. Something I've noticed is that many games allow you to delve deeper into the folklore of the story through collectible items, etc.