If a game isn't fun as a game (and not as whatever art fluff is attached to the actual game), that's more or less the equivalent of entering a three-legged horse in a race. Yeah, it might eventually hobble its way to the finish line and satisfy 'being good enough to justify its own existence', but there's some pretty obvious reasons why it's always going to fall short of just about any halfway-competent fun game, and some equally obvious reasons why the same game would be much better served by bothering to make the 'game' part fun.
Which isn't to say that it isn't a good deal more complicated than 'be as fun as possible at all times'. There are plenty of ways to pace the fun in a game, whether it's a moment-to-moment absolute blast, a longer, more passive 'consistently enjoyable', or even/especially using a buildup-payoff model, where the payoff is made more rewarding than it would be otherwise because the path there was long, frustrating, or whatever. But if it isn't designed such that ultimately 'fun' is the main focus, you've got a bad game, and the best atmospheres and stories in the world aren't going to make a whit of difference.