I'm no expert, but I believe that how much story matters depends on the game. You could easily make a platformer with next to no story. You can't do that for a visual novel kind of game. Gameplay though, will always be an important part of a game. Story for any game can be found online no problem but the gameplay itself can only truly be enjoyed by playing it. most games who are seen as only being good in areas outside of gameplay will usually have people watch videos of it instead of playing it since they don't have to bother with boring or annoying mechanics.
When making a game in general, I feel that the game idea and gameplay should be the first thing to focus on. Even in a story-oriented game like what you were participating in, knowing how the game will progress or if it works to begin with is more important. You probably shouldn't finish the whole of gameplay and complete every mechanic before starting the story if you want it to be a big part of the game from the get-go, so having some outline for the story and knowing how much it will tie in with gameplay might be a good way to go about it.