Like if it has side quests aside the main story, a town to explore, would it not be story focused even if there's an ongoing story? Does the gameplay have to affect the story? Could a level based game with cutscenes in the beginning and end of each level but gameplay in between count?

A story-focused game is when the narrative is the main focus, with gameplay serving to enhance the story rather than dominate it.

Ah, I see! Thank you very much!